To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32°. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 35°. Estimate the height of the mountain. (Round your answer to the nearest foot.)

Question
Asked Sep 29, 2019
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To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32°. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 35°. Estimate the height of the mountain. (Round your answer to the nearest foot.)

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Expert Answer

Step 1

First we draw a rough sketch from the given information.

Let height of the mountain is h.

32
35
1000
C
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32 35 1000 C

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Step 2

In triangle ABC, 

AB/BC =tan 35

h/BC=tan35

BC=h/tan35

32
35
В
1000
C
help_outline

Image Transcriptionclose

32 35 В 1000 C

fullscreen
Step 3

In triangle ABD

AB/BD= tan 32

h/BD=t...

A
32
35
C
1000
C
help_outline

Image Transcriptionclose

A 32 35 C 1000 C

fullscreen

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