Name ______

Tangent Table
Measurement of angle / Tangent of angle
5° / 0.09
7.5° / 0.13
10° / 0.18
12.5° / 0.22
15° / 0.27
17.5° / 0.31
20° / 0.36
22.5° / 0.41
25° / 0.47
27.5° / 0.52
30° / 0.58
32.5° / 0.63
35° / 0.70
37.5° / 0.77
40° / 0.84
42.5° / 0.92
45° / 1.0

How big is your Mountain?

Mountains come in various shapes and sizes. We are lucky to live in California which is rich in mountain ranges. In this activity, you will measure our local mountain, Mt Boney. The official name for Mt. Boney is actually Sandstone Peak. Sandstone Peak is the highest point in the Santa Monica Mountains and on a clear day you can see several of the Channel Islands. The mountain is not actually composed of sandstone, like the name suggests, but andesite. To measure Mt. Boney we are going to use our knowledge of triangles and a tool called an astrolabe. The astrolabe will help us measure angles.

Example #1

You are curious about how tall a tree is. You are able to stand 100 ft. away from the tree and see the top of the tree. You use your astrolabe to determine the angle as 30°. Using the tangent table and the steps below, determine the height of the tree.

1) How many feet away from the tree are you? ______

2) What is the angle you measured to the top of the tree? ______

3) Using the tangent table what is the tangent of your angle equal to? ______

4) Plug in your values in the following equation:

______X ______= ______

Tangent of angle Dist. From object Height of tree

Trial #1

Before we measure Mt Boney we need to practice using the astrolabe and our calculations. We will measure the height of the NPHS baseball flagpole. We will need to measure the same values as we were given in Example 1. Remember you should measure the angle from the top of your yard stick.

1) How many feet away from the flagpole are you? ______

2) What is the angle you measured to the top of the flagpole? ______

3) Using the tangent table what is the tangent of your angle equal to? ______

4) Plug in your values in the following equation:

______X ______= ______

Tangent of angle Dist. From object Height of flagpole

Trial #2

Now we will measure the height of Mt Boney. You will need to measure the same values as in Example 1 and Trial 1 to complete the necessary calculations. You are currently standing 3.558 miles from Sandstone Peak.

1) How many feet away from the mountain are you? ______

2) What is the angle you measured to the top of the mountain? ______

3) Using the tangent table what is the tangent of your angle equal to? ______

4) Plug in your values in the following equation:

______X ______= ______

Tangent of angle Dist. From object Height of mountain

Conclusion Questions

1)  What is the name of the Mountain you measured?

2)  What type of rock is the mountain made of?

3)  Your teacher will now tell you the actual height of the mountain. How far off are you? Come up with 3 possible sources of error?

4)  Calculate your percent error using the following formula:

Review Questions

4) What are the three types of stress? Describe each.

5) What are the three types of faults? Describe each.

6) Define Orogenesis.

7) What are the three types of mountains from the notes? Describe each.