   Chapter 1, Problem 52P

Chapter
Section
Textbook Problem

A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.0°. Find the mountain’s height, neglecting the height of the woman’s eyes above the ground. Hint: Distances from the mountain (x and x − 1 km) and the mountain’s height are unknown. Draw two triangles, one for each of the woman’s locations, and equate expressions for the mountain's height. Use that expression to find the first distance x from the mountain and substitute to find the mountain’s height.

To determine
The height of the mountain by neglecting the height of the woman’s eyes above the ground.

Explanation

The first position of the woman from the mountain.

Given Info: The angle of elevation of the mountain from the first position of the woman is 12° .

After walking 1km distance the angle of elevation is 14° .

Explanation:

The diagram for the angle of elevation for the two positions is,

From the diagram, the expression of the height of the mountain for the first angle of elevation is,

y=xtan(12°)

• x is the first position of the woman.
• y is the height of the mountain,

And that for the second angle of elevation is,

y=(x1)tan(14°)

Calculating the first position of the woman from the mountain by equation the both expression of the height of the mountain,

(x1)tan(14°)=xtan(12)x(tan14°tan12°)=tan14°

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