A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 2.62 km closer to the mountain on level ground, she finds the angle to be 14.0° (a) Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. Hint: Use two triangles. Select variable names for the mountain height (suggestion: y) and the woman's original distance from the mountain (suggestion: x) and label the picture. (b) Using the labeled picture and the tangent function, write two trigonometric equations relating the two selected variables. (Use the following as necessary: x and y. Do not enter units in your answers.) tan(12°) = tan(14°) =

College Physics
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ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Introduction
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A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 2.62 km closer to the mountain on level ground, she finds the angle to be 14.0°

(a) Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. Hint: Use two triangles. Select variable names for the mountain height (suggestion: y) and the woman's original distance from the mountain (suggestion: x) and label the picture.

(b) Using the labeled picture and the tangent function, write two trigonometric equations relating the two selected variables. (Use the following as necessary: x and y. Do not enter units in your answers.)
 
tan(12°) = 
 
 

tan(14°) = 
 
 

(c) Find the height y of the mountain by first solving one equation for x and substituting the result into the other equation.
y =  km
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