Serway & Jewett — Physics and Measurement: Problem 38

A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as $12.0^{\circ}$. After walking $1.00\text{ km}$ closer to the mountain on level ground, she finds the angle to be $14.0^{\circ}$. (a) Draw a picture of the problem, neglecting the height of the woman’s eyes above the ground. Hint: Use two triangles. (b) Using the symbol $y$ to represent the mountain height and the symbol $x$ to represent the woman’s original distance from the mountain, label the picture. (c) Using the labeled picture, write two trigonometric equations relating the two selected variables. (d) Find the height $y$.