Manuel

1

Distancelater

2

Mountain Hikers

Huntington North High School

450 MacGahan St.

Maria Scott ~ Brad Young ~ Charleston Dydasco ~ Nathan Pike

How to use our Device: In order to use our device, you need to understand some theorems.

Now, we have written all the theorems you need to know in order to calculate the measurements precisely. You move the swivel to the top of mountain or object, and then you use the angle to put it on your triangle. Then you need to know the distance of at least one leg of your triangle. Lastly, use one of the theorems to find out the height or length of the mountain.

Our device has everything needed to know how to do these tasks.

Ruler

Swivel protractor

3

What our Device Does:

Our device is an easy to use object. It has many uses such as measuring angles and telling distances. If you are tired and only plan on climbing a small hill or ambitious and want to climb a tall hill, you can use our device to measure the length of the hill and how far you will be walking. Special ways to use this device include seeing a certain angle and how far away something is. If you are wondering how we can do all of this in one small product, it is so easy to explain. Included in our product:

Protractor

Swivel

Ruler

Calculator

Notepad

List of formulas If you are looking for precise triangles and direct measurements, the square shape helps it tell correct 45 degree angles, 90 degree angles, and even 30 and 60 degree angles when looking at the protractor. We used our imagination and innovation in creating it and it helps in any climbing situation. (Unless you’re stuck) Even if you don’t think you need the device, you should really think again. Here is a couple of ways how to use it:

If you need to calculate a specific angle, you can find out what it is with our device. You can use this device to find out distances between you and your climbing destination. You can use the notepad to either write down notes or work own different calculations or

theorems. The calculator included can create an easy access to finding out Sine, Cosine, and

Tangent for all Geometry lovers. It also has different formulas for all types of right triangles for any mountain. Shows how to calculate a distance. You don’t have to memorize anything at all.

If you want to fully appreciate your hiking, use our device. It can calculate how many miles you have hiked, measure the angles and distance of what you have climbed, and it is easily portable and assessable.

4

Formulas for Calculating Angles/Distances:

Pythagorean Theorem o A2+B2=C2

Sine o Opposite/Hypotenuse

Cosine o Adjacent/Hypotenuse

Tangent o Opposite/Adjacent

60 30 90 Triangles o To find hypotenuse: 2 X short leg o To find longer leg: square root of 3 X short leg

45 45 90 Triangles o To find hypotenuse: square root of 2 X short leg

5

Practice Problems

1. Tangent and Cosine

You climbed up a mountain and back down on the other side. You measured the width

of the mountain with your device. You know you climbed 61.09 meters down the mountain. How

many meters did you climb up and down throughout the

whole mountain? Use the device to find the angle of x.

2. Sine

You are going on a hike by yourself. Your friends back home want the dimensions of

your whole mountain when you get back. Use your device to help find angles and check

calculations.

.

.

6

3. 60 30 90 Triangles

You have been climbing all day and are very tired.

However, you told your friends you would climb this

mountain too. You want to climb the shortest side. Use

the device to find out what side you will climb, x or w.

Also find out y.


You want to climb this mountain. You know that is is 400 feet up. How many feet

will it be going down? Using the square shape in our device, you can find out the dimensions of

the mountain.

7


Mark and Emily are wanting to climb a mountain that is steep. Use the device to help

calculate the non-given angles/ lengths. Find the steeper mountain.

6. Pythagorean Theorem

You want to climb the longest side of the mountain. Use the Pythagorean theorem to find

out which side you will climb?

8

Practice Problems with Answers

1. Tangent and Cosine

You climbed up a mountain and back down on the other side. You measured the width

of the mountain with your device. You know you climbed 61.09 meters down the mountain. How

many meters did you climb up and down throughout the

whole mountain? Use the device to find the angle of x.

x=.269 or 15.1 degrees

y= 52.25

ANSWER: 113.34 m

Using Cosine to find y: adjacent/ hypotenuse

14.1= .9699

.9699= y / 61.09

52.25= y

Using Tangent to find x: opposite/ adjacent

x = 14.1 / 52.251191

x = .269

9

2. Sine

You are going on a hike by yourself. Your friends back home want the dimensions of

your whole mountain when you get back. Use your device to help find angles and check

calculations.

w= 56 degrees

x= 34 degrees

y= 9.9 m

z= 6.7 m

Found x using device: 34 degrees.

Using sine to find z= opposite/hypotenuse

34= .5592

.5592 = z/12

6.7 = z

Find w knowing the sum of the angles of a triangle

equal 180 degrees.

34+90 = 124

180- 124 = 56

Therefore; w = 56 degrees

Find y using tangent: opposite/ adjacent

56 = 1.4826

1.4826 = y/6.7

9.9= y

10


You have been climbing all day and are very tired.

However, you told your friends you would climb this

mountain too. You want to climb the shortest side. Use

the device to find out what side you will climb, x or w.

Also find out y.

y = 30 degrees

w = 30 ft.

x = 25.98 ft.

Longer leg: square root of 3 X short leg

How to find hypotenuse= 2 X shorter leg


You want to climb this mountain. You know that is is 400 feet up. How many feet

will it be going down? Using the square shape in our device, you can find out the dimensions of

the mountain.

Putting the square shape up, you can

easily tell that it is a 45 45 90 triangle. Therefore;

y= 45 degrees

x= 45 degrees

z = 400 ft.

w = 565.69 ft.

To find the hypotenuse::

square root of 2 X leg

1.4142135623731 X 400 = 565.69 feet

11

5. 60 30 90 Triangles and Cosine

Mark and Emily want to climb a mountain that is steep. Use the device to help calculate the non-

given angles/ lengths. Find the steeper mountain.

X= 30 degrees A=48 degree

Y=45 meters B=29 meters

Z=26 meters C=39 meters

Triangle 1

Hypotenuse = 2 X short leg

52 = 2 x z

Z = 26 m

Longer leg = square root of 3 X short leg

Y = 1.732050808 X 26

Y = 45 m

Triangle 2

Find a knowing the sum of the angles of a triangle equal 180 degrees.

42+90 = 132

180- 124 = 48

Therefore; a = 48 degrees

Cosine = adjacent/ hypotenuse

.669130606 = 26/c

39 = c

Tangent = opposite / adjacent

1.110612515 = b / 26

29 = b

You want to climb the first mountain.

12

6. Pythagorean Theorem

You want to climb the longest side of the mountain. Use the Pythagorean theorem to find

out which side you will climb?

A squared +B squared = C squared.

20 squared + 40 squared = C squared.

400 +1600= C squared.

2000=c squared.

44.7m=c Answer= X

Manuel

Documents

Transcript of Manuel