Right s and trigonometry7 Pythagorean Theorem the determine right triangles6 Pythagorean Theorem, solve sides 5 WP: Pythagorean Theorem4 Special Right Triangles3 Sine, Cosine and Tangent ratios2 Trig to solve sides in a 1 WP: TrigonometryUnit Review

7 Pythagorean Theorem to determine right triangle

What is the proper pronunciation for the second day of the week?a) TEE-USE-DAY

b) CHOOSE-DAY

c) TWOS-DAY

d) None of the above

7a Pythagorean Theorem to determine right triangle

If the Pythagorean theorem works for 3 numbers (“c” will always be the largest), then these values form a right triangle.

If a2+b2=c2 is true, then it is a right triangle

Keep in mind that C will ALWAYS be the longest side

7b Pythagorean Theorem to determine right triangle

Ex1. How many of the triples below could be sides of a right triangle?

(14, 48, 49)

(33, 56, 65)

(9, 41, 40)

(45, 36, 27)

7c Pythagorean Theorem to determine right triangle

Ex2. Which of the triangles described in the table is a right triangle?

Side 1 Side 2 Side 3

Triangle Q 10 8 6

Triangle R 11 8 19

Triangle S 10 8 164

Triangle T 110 11 10

6 Pythagorean theorem

A Whip!

6a Pythagorean theoremRemember this….. a2+b2=c2

What does the letter “c” represent? __________Hypotenuse

What does “a” and “b” represent? _______________The legs of the

This only applies to right triangles!

__

The side opposite the right angle is the __________

Hypotenusec

hypotenuse

6b Pythagorean theorem

10

8

Ex1. Find the missing side of the triangle

82+102=h2 From Pyth theorem

64+100= h2 Solve

164= h2

Ex2. ABC is a right triangle with hypotenuse c and legs of length a and b. If b = 8 and c 10, then a = _____.

10

8

a

5 WP: Pythagorean theoremImagine a bridge that spans a canyon of two miles. (5280 feet = 1 mile)

2 mile bridge

Unfortunately they forgot to place expansion joints into the bridge and when it gets hot, the bridge expands exactly one foot.

How high does the bridge bow upward with this expansion?2 mi + 1 foot bridge

What is the height?(Approx)

5a WP: Pythagorean theorem

Draw a picture and label it!!!!The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram below. The construction cost has been estimated at $100 per linear foot. Find the estimated cost for constructing the street.

(New

Stre

et)

Main St.

N. B

lvd

3 mi.

8 mi.

82+32=c2

64+9=c2

73=c2

73=c

The new road is 73 mi.

(73)(5280) (x) by feet/mi.

(45112.339)($100)

$4,511,233.90 Approx

5b WP: Pythagorean theoremEx2. Janina used the diagram to compute the distance from Ferris to Dunlap to Butte.

How much shorter is the distance directly from Ferris to Butte than the distance Janina found?

20 mi

21 mi

Ferris

Dunlap Butte

?

4 Special Right Triangles

Do you have a calculator with Sin, Cos

& Tan buttons?

4a 45-45-90 Triangles

||

=

What are the degree measures of this ?

45°

45°

If we had a leg length of 1, what is the hypotenuse?(Use Pythagorean theorem) _______

1

12

If we had a leg length of 10, what is the hypotenuse? ______

0

102

Using the Pythagorean theorem we can conclude:

P

P||

= P2For all 45-45-90 s

4b 30-60-90 Triangles

60°

30°

5

10w

Using the Pythagorean theorem, find “w”! NOW!!!

52+w2=102

25+w2=100

w2=75w=75

75/ \

25 3

53

53

60°

Using the Pythagorean theorem, we can conclude:

P

2PP3For all 30-60-90 triangles

4c 45-45-90 Triangles

Ex1. In ABC, A is a right angle and mB=45°. If AB=36 feet, find BC.

A B

C

45°36 ft

BC=362

4d 30-60-90 Triangles

30°

60°

P

2PP3

Ex2. In a 30-60-90 triangle, the hypotenuse is 28 feet,

What is the shorter leg? ___________14 feet

What is the longer leg? ___________143

28

14

3 Sine, Cosine & Tangent ratios

Bible trivia time…….How many years did Moses wonder the desert before he entered the promised land?

Moses reached the promised land, however, God forbade him entrance.

How many wise men went to see Jesus?

We don’t know, we only know of the mention of three gifts.

25 point reward for turning in calculators that are

missing from my class…!

3a Sine, Cosine & Tangent ratios

Some Old Hippie, Came A Hopping, Through Our Alley

S C Tine os an= = =OppositeHypotenuse

AdjacentHypotenuse

OppositeAdjacent

Remember this and you will have it easy…!

Adjacent - The leg touching the angle

Opposite - Leg opposite the angle

Hypotenuse - Side opposite the right angle

3b Sine, Cosine & Tangent ratios

A

BC9

12 15

Is this a right ? _________yes

Why? _______________Since a2+b2 = c2

What is the Sine of A? ___________9/15 = 3/5

What is the Cos of A? ___________12/15 = 4/5

What is the Tan of A? ___________9/12 = 3/4

S C TO A OH H A

3c Sine, Cosine & Tangent ratios

3d Sine, Cosine & Tangent ratios

2 Trig to solve sides in a

I am thinking of two common objects, they both carry out the same function, but one has thousands of moving parts and the other has no moving parts. What are these items?

Hurry, times a wasting….!

2a Trig to solve sides in a

Remember

27° 7

x

Solve for x.

Which side are we looking for? a o h

Which side do we have? a o h

Since Cos uses “a” and “h”, we are going to use the Cos function

Cos27= 7x

(cos27) (x)= 7 Cross Mulitply x7.86

PS. means approx equal

S C TO A OH H A

2b Trig to solve sides in a

25°7

x

Solve for x

What sides are we working with in reference to the angle? O & A

Tan25= X7

(Tan 25) (7) = x

3.26 x

2c Trig to solve sides in a Ex3. Given A = 47 and c = 12, find a, to the nearest tenth.

A

BC a

b c47°

12

1 WP: Trigonometry

What do veterinarians usually call little cats with white, black, red and cream colored coats?

1a WP: Trigonometry

1b WP: TrigonometryEx1. A slide 3.4 m long makes an angle of 35 with the ground. How high is the top of the slide above the ground?

35°

?

3.4m

1c WP: TrigonometryEx2. A ladder leans against a building forming an angle of 60 with the ground. The base of the ladder is 4 feet from the building. Find the length of the ladder.

1d WP: TrigonometryEx3. A ladder 14 feet long makes an angle of 53 with the ground as it leans against a barn. How far up the barn does the ladder reach?

Unit 8 Review

If a2+b2=c2 is true, then it is a right triangle.

Pythagorean Theorem – Given length of two sides. c

P

P||

= P2

For all 45-45-90 s

60°

P

2PP3

For all 30-60-90 triangles

When give a Degree and the length of a side.

S C TO A OH H A