Angle of elevation question

Question

Angles of elevation to an airplane are measured from the top and the base of a building that is 20 m tall. The angle from the top of the building is 38°, and the angle from the base of the building is 40°. Find the altitude of the airplane. (Round your answer to two decimal places.)

Answer 1

Use the definition of tangent: opposite/adjacent.

 

For the right triangle starting at the bottom of the building, tan 40 = h/x, where h is the height of the plane we are trying to find and x is the horizontal distance to the plane, also unknown.

For the right triangle starting at the top of the building, tan 38 = (h-20)/x, since the height of the plane relative to the top of the building is only h-20.

Now divide the two equations, and x cancels:

 

tan 38 / tan 40 = (h-20)/x / (h/x) = (h-20)/h = 1 - 20/h

 

Now just solve this for h. You can do it!

Answer 2

Hi Lauren;

Throughout all of the mathematics I took in high school and college, I never encountered such a question.  This is my guess.  Please wait to see what other Wyzants say before entering this into your homework.

 

At the base of the building, the angle is 40-degrees.

At 20-meters above this, the angle is 38-degrees.

We need the value of the height at 0-degrees.

The ratio of...

change-of-degrees

change-of-height

 

2-degrees

20-meters

 

1-degree

10-meters

 

40-degrees is 400-meters.

 

I am suspicious of my answer because we do not need the instruction of Round your answer to two decimal places.