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Angle of elevation 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.)
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2 Answers

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!

Comments

Hi Andre;
I cannot solve for h as it represents the height of the plane.
I do not understand the way you understand this.
The way I understand this is the 20-feet building is opposite the 102-degree angle, 180-(40+38)=102.  The building is the hypotenuse of the triangle which does NOT include the side which represents the height of the airplane.  That is a different triangle.
 
Hi Vivian,
I'm not sure why you add 40 and 38 degrees, as they refer to different triangles. These are angles of elevation, measured relative to the horizontal, so there are two right triangles, 40-50-90 and 38-52-90. 

Comment

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.