Sine, Cosine, Tangent Applications

The Sine, Cosine and Tangent functions are often applied to real world scenarios.

Example 1

What is the height of the tree on the left?

tan(16°)= 14/height
height =14/tan(16°) = 48.8 "

Example 2

At 57" from the base of a building you need to look up at 55° to see the top of a building. What is the height of the building?

tan(55°) = height/57
height = 57 × tan(55°) = 81.4"

Example 3

The angle of elevation from a point 43 feet from the base of a tree on level ground to the top of the tree is 30°. What is the height of the tree? Round your answer to the nearest tenth

Step 1

First, you should draw and label a picture of this word problem.

Step 2

The illustration

real world sohcahtoa
Rest of Step
Example 4

If the angle of elevation to the top of a tree is 20°. How far are you away from the tree, if the tree's height is 31 feet? Round your answer to the nearest tenth

Step 1

First, you should draw and label a picture of this word problem.

Step 2

The illustration

Rest of Step
Example 5

If the angle of elevation to the top of a tree is 65°. How far are you away from the tree, if the tree's height is 27 feet? Round your answer to the nearest tenth

Step 1

First, you should draw and label a picture of this word problem.

Step 2

The illustration

Rest of Step