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FIRST STEP : Find the height of the tree.

1) Firstly, we measured the height of the tree. One of our groups member stood

13 feet from the back of the tree.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 137.

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5) Finally, we have reached the angle of elevation of the top of the tree from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 47.

SECOND STEP : Find the height of the Academic block.

1) Due to the distance between the tree and the academic block is so near, so we

have decided to measure the height of the block 24.06 feet from the block.

2) Therefore, the angle of elevation of the top of the block from the observers

eye by deducting the initial angle with 90is 54.

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Solution :

To calculate the distance between the top of the tree and the top of the building, we

have divide it to three step.

First Step : Find the height of the tree

1) The angle of elevation of the top of the tree from the observers eye is 47.

2) From the angle of elevation, we used the right triangle trigonometry to find the

height of the tree.

3) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 47=

= 13ft. x (tan 37)

= 13.94 ft.

4) The value of is added with the observers eye level from the groundwhich is 4.6 feet.

= 13.94 ft.

Observers eye level from the ground= 4.6 ft.

The height of the tree is:

13.94 ft. + 4.6 ft. = 18.54 ft.

5) Thus, the height of the tree is 18.54 feet.

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Second Step : Find the height of the Block

1) Then, we find the height of the academic block.

2) The angle of elevation of the top of the academic block from the observers eye is 54.

3) From the angle of elevation, we used the right triangle trigonometry to find the

height of the block.

4) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 54=

= 24.06 ft. x (tan 54)

= 33.12 ft.

5) The value of is added with the height of the observer which is 4.6 feet.

= 33.12 ft.

Observers eye level from the ground= 4.6 ft.

The height of the block is:

33.12 ft. + 4.6 ft. = 37.72 ft.

6) Thus, the height of the block is 37.72 feet.

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Third Step : Find the distance between the tree and the academic block.

1) From the first step and the second step, we have found the height of the tree and the

block which are 18.54 ft. and 37.72 ft.

2) From the heights, we used Phytagoras Theorem to find the distance.

Let the opposite side be x.

3) To find x , we have to deducted the height of the academic block with the height of the

tree.

Height of the block : 37.72 ft.

Height of the tree : 18.54 ft.

x = 37.72 ft.18.54 ft.

= 19.18 ft.

4) Then, by using Pythagorean Theorem :

Let the distance between the top of the tree and the block be y.

=

y =

= 22.14 ft.

The distance between the top of the tree and the academic block is 22.14 feet,

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b) The Distance between the academic block and the top of the hut.

As for this task, we have found two method to solve it.

Method I

1) Firstly, we measured the height of the academic block from the hut. One of our

groups member stood 28.2 feet from the block at the hut.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 144.

5) Finally, we have reached the angle of elevation of the top of the block from

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the observers eye by deducting the initial angle with 90. Therefore, the angle

is 54.

6) Next, we measured the height of the hut from the academic block. One of our

groups member stood 28.2 feet from the hut at the block.

7) The eye level of the observer from the ground has been measured which is 4.6

feet.

8) Another observer has taken the reading of the angle which is 115.

9) Finally, we have reached the angle of elevation of the top of the hut from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 25.

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Solution :

Method I

To calculate the distance between the top of the hut and the top of the academic block,

we have divide it to three step.

First Step : Find the height of the hut

1) The angle of elevation of the top of the hut from the observers eye is 25.

2) From the angle of elevation, we used the right triangle trigonometry to find the

height of the hut.

3) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 25=

1= 28.2 ft. x (tan 25)

= 13.15 ft. (round off to two decimal places)

= 13 ft.

4) The value of is added with the height of the observer which is 4.6 feet.

1= 13 ft.

Observers eye level from the ground= 4.6 ft.

The height of the hut is:

13 ft. + 4.6 ft. = 17.6 ft.

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5) After rounded off to two decimal places, the height of the hut is 18 feet.

Second Step : Find the height of the Block

1) Then, we find the height of the academic block from the hut.

2) The angle of elevation of the top of the academic block from the observers eye is 54.

3) From the angle of elevation, we used the right triangle trigonometry to find the

height of the block.

4) By using the tangent ratios:

tan =

Let the opposite side be x2.

tan 54=

= 28.2 ft. x (tan 54)

= 38.81 ft.

5) The value of is added with the observers eye level from the groundwhich is 4.6 feet.

= 38.81 ft.

Observers eye level from the ground= 4.6 ft.

The height of the block is:

38.81 ft. + 4.6 ft. = 43.41 ft.

6) After rounded off to two decimal places, the height of the block is 43 feet.

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Third Step : Find the distance between the hut and the academic block.

1) From the first step and the second step, we have found the height of the hut and the

block which are 18 ft. and 43 ft.

2) From the heights, we used Pythagoras Theorem to find the distance.

Let the opposite side be z.

3) To find z , we have to deducted the height of the academic block with the height of the

tree.

Height of the block : 43 ft.

Height of the tree : 18 ft.

z = 43 ft.18 ft.

= 25 ft.

4) Then, by using Pythagorean Theorem :

Let the distance between the top of the hut and the block be y.

=

y =

= 37.69 ft.

The distance between the top of the tree and the academic block is 37.69 feet.

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Method II

First step : Height of the Block.

1) Firstly, we measured the height of the block. One of our groups member stood

in the middle of the academic block and the hut which the length is 14.1 feet.

from the block.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 160.

5) Finally, we have reached the angle of elevation of the top of the block from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 70.

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Second step : Height of the Hut.

1) Next, we measured the height of the hut. One of our groups member stood in

the middle of academic block and the hut which is the length is 14.1 feet from

the hut.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 133.

5) Finally, we have reached the angle of elevation of the top of the hut from

the observers eye by deducting the initial angle with 90. Therefore, the angle

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is 43.

Solution :

Method II

To calculate the distance between the top of the hut and the top of the academic block,

we have divide it to three step.

First Step : Find the height of the hut

1) The angle of elevation of the top of the hut from the observers eye is 43.

2) From the angle of elevation, we used the right triangle trigonometry to find the

height of the hut.

3) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 43=

1= 14.1 ft. x (tan 43)

= 13.15 ft.(round off to two decimal places)

= 13ft.

4) The value of is added with the height of the observer which is 4.6 feet.

1= 13 ft.

Observers eye level from the ground = 4.6 ft.

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The height of the hut is:

13 ft. + 4.6 ft. = 17.6 ft.

5) After rounded off to two decimal places, the height of the hut is 18 feet.

Second Step : Find the height of the Block

1) Then, we find the height of the academic block from the hut.

2) The angle of elevation of the top of the academic block from the observers eye is 70.

3) From the angle of elevation, we used the right triangle trigonometry to find the

height of the block.

4) By using the tangent ratios:

tan =

Let the opposite side be x2.

tan 70

=

= 14.1 ft. x (tan 70)

= 38.74 ft.

5) The value of is added with the observers eye level from the ground which is 4.6 feet.

= 38.74 ft.Observers eye level from the ground = 4.6 ft.

The height of the block is:

38.74 ft. + 4.6 ft. = 43.34 ft.

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6) After rounded off to two decimal places, the height of the block is 43 feet.

Third Step : Find the distance between the hut and the academic block.

1) From the first step and the second step, we have found the height of the hut and the

block which are 18 ft. and 43 ft.

2) From the heights, we used Phytagoras Theorem to find the distance.

Let the opposite side be z.

3) To find z , we have to deducted the height of the academic block with the height of the

tree.

Height of the block : 43 ft.

Height of the hut : 18 ft.

z = 43 ft.18 ft.

= 25 ft.

4) Then, by using Pythagorean Theorem :

Let the distance between the top of the hut and the block be y.

=

y =

= 37.69 ft.

The distance between the top of the hut and the academic block is 37.69 feet.

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c) The distance between the top of the flagpole and the top of the tree.

As for this task, we have found three method to solve it.

Method I

For this task, we have divided this method to three steps.

First step : Find the height of the tree

1) Firstly, we measured the height of the tree. One of our groups member stood

In the middle of the tree and the flagpole which is 12.5 feet from the tree.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 150.

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5) Finally, we have reached the angle of elevation of the top of the tree from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 60.

Second step : Find the height of the flagpole.

1) Then, we have to find the height of the flagpole . One of our groups member

stood in the middle of the tree and the flagpole which is 12.5 feet from the

flagpole.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

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4) Another observer has taken the reading of the angle which is 141.

5) Finally, we have reached the angle of elevation of the top of the tree from

the observers eye by deducting the initialangle with 90. Therefore, the angle

is 51.

Solution :

Method I

To calculate the distance between the top of the flagpole and the top of the tree, we

have divide it to three step.

First Step : Find the height of the tree

1) The angle of elevation of the top of the tree from the observers eye is 60.

2) From the angle of elevation, we used the right triangle trigonometry to find the

height of the tree.

3) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 60=

1= 12.5 ft. x (tan 60)

= 21.65 ft.

4) The value of is added with the height of the observer which is 4.6 feet.

1= 21.65 ft.

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15.44 ft. + 4.6 ft. = 20.04 ft.

6) After rounded off to two decimal places, the height of the flagpole is 20 feet.

Third Step : Find the distance between the tree and the flagpole.

1) From the first step and the second step, we have found the height of the tree and the

flagpole which are 26 ft. and 20 ft.

2) From the heights, we used Phytagoras Theorem to find the distance.

Let the opposite side be z.

3) To find z , we have to deducted the height of the tree with the height of the flagpole.

Height of the tree : 26 ft.

Height of the flagpole : 20 ft.

z = 26 ft.20 ft.

= 6 ft.

4) Then, by using Pythagorean Theorem :

Let the distance between the top of the flagpole and the tree be y.

=

y =

= 25.71 ft.

The distance between the top of the tree and the flagpole after round off

to two decimal place is 26 feet.

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Method II

First step : Find the height of the tree

1) Firstly, we measured the height of the tree from the flagpole. One of our

groups member stood 25 feet from the tree at the flagpole.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 130.

5) Finally, we have reached the angle of elevation of the top of the tree from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 40.

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Step 2 : Find the height of the flagpole

6) Next, we measured the height of the flagpole from the tree. One of our

groups member stood 25 feet from the flagpole at the tree.

7) The eye level of the observer from the ground has been measured which is 4.6

feet.

8) Another observer has taken the reading of the angle which is 122.

9) Finally, we have reached the angle of elevation of the top of the hut from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 32.

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Solution :

Method II

To calculate the distance between the top of the flagpole and the top of the tree, we

have divide it to three step.

First Step : Find the height of the tree

1) The angle of elevation of the top of the tree from the observers eye is 40.

2) From the angle of elevation, we used the right triangle trigonometry to find the

height of the tree.

3) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 40=

1= 25 ft. x (tan 40)

= 20.98 ft.

4) The value of is added with the height of the observer which is 4.6 feet.

1= 20.98 ft.

Observers eye level from the ground = 4.6 ft.

The height of the tree is:

20.98 ft. + 4.6 ft. = 25.58 ft.

5) After rounded off to two decimal places, the height of the tree is 26 feet.

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Second Step : Find the height of the Flagpole

1) Then, we find the height of the flagpole.

2) The angle of elevation of the top of the flagpole from the observers eye is 32.

3) From the angle of elevation, we used the right triangle trigonometry to find the

height of the flagpole.

4) By using the tangent ratios:

tan =

Let the opposite side be x2.

tan 32=

= 25 ft. x (tan 32)

= 15.62. ft.

5) The value of is added with the observers eye level from the ground which is 4.6 feet.

= 15.62 ft.

Observers eye level from the ground = 4.6 ft.

The height of the flagpole is:

15.62 ft. + 4.6 ft. = 20.22 ft.

6) After rounded off to two decimal places, the height of the flagpole is 20 feet.

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Third Step : Find the distance between the tree and the flagpole.

1) From the first step and the second step, we have found the height of the tree and the

flagpole which are 26 ft. and 20 ft.

2) From the heights, we used Phytagoras Theorem to find the distance.

Let the opposite side be z.

3) To find z , we have to deducted the height of the tree with the height of the flagpole.

Height of the tree : 26 ft.

Height of the flagpole : 20 ft.

z = 26 ft.20 ft.

= 6 ft.

4) Then, by using Pythagorean Theorem :

Let the distance between the top of the tree and the flagpole be y.

=

y =

= 25.71 ft.

The distance between the top of the tree and theflagpole after round off

to two decimal place is 26 feet.

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Method III

First step : Find the height of the tree

1) Firstly, we measured the height of the tree. One of our groups member stood

10 feet from the back of the tree.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

4) Another observer has taken the reading of the angle which is 155.

5) Finally, we have reached the angle of elevation of the top of the tree from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 65.

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Second Steps : Find the height of the flagpole

1) Next, we measured the height of the flagpole. One of our groups member

stood 8 feet from the back of the flagpole.

2) The eye level of the observer from the ground has been measured which is 4.6

feet.

8) Another observer has taken the reading of the angle which is 152.

9) Finally, we have reached the angle of elevation of the top of the flagpole from

the observers eye by deducting the initial angle with 90. Therefore, the angle

is 62

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Solution :

Method III

To calculate the distance between the top of the flagpole and the top of the tree, we

have divide it to three step.

First Step : Find the height of the tree

1) The angle of elevation of the top of the tree from the observers eye is 65.

2) From the angle of elevation, we used the right triangle trigonometry to find the

height of the tree.

3) By using the tangent ratios:

tan =

Let the opposite side be x.

tan 65=

1= 10 ft. x (tan 65)

= 21.45 ft.

4) The value of is added with the height of the observer which is 4.6 feet.

1= 21.45 ft.

Observers eye level from the ground = 4.6 ft.

The height of the tree is:

21.45 ft. + 4.6 ft. = 26.05 ft.

5) After rounded off to two decimal places, the height of the tree is 26 feet.

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Second Step : Find the height of the Flagpole

1) Then, we find the height of the flagpole.

2) The angle of elevation of the top of the flagpole from the observers eye is 62.

3) From the angle of elevation, we used the right triangle trigonometry to find the height of the

flagpole.

4) By using the tangent ratios:

tan =

Let the opposite side be x2.

tan 62=

= 8 ft. x (tan 62)

= 15.05 ft.

5) The value of is added with the observers eye level from the ground which is 4.6 feet.

= 15.05 ft.

Observers eye level from the ground = 4.6 ft.

The height of the flagpole is:

15.05 ft. + 4.6 ft. = 19.64 ft.

6) After rounded off to two decimal places, the height of the flagpole is 20 feet.

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Third Step : Find the distance between the tree and the flagpole.

1) From the first step and the second step, we have found the height of the tree and the

flagpole which are 26 ft. and 20 ft.

2) From the heights, we used Phytagoras Theorem to find the distance.

Let the opposite side be z.

3) To find z , we have to deducted the height of the tree with the height of the flagpole.

Height of the tree : 26 ft.

Height of the flagpole : 20 ft.

z = 26 ft.20 ft.

= 6 ft.

4) Then, by using Pythagorean Theorem :

Let the distance between the top of the hut and the block be y.

=

y =

= 25.71 ft.

The distance between the top of the tree and the academic block after round off

to two decimal place is 26 feet.