A woman measures the angle of elevation from her current location to a mountaintop to be 12.0°. After walking 1.20 km closer to the mountain on level ground, she gauges the angle again and finds it to be 14.0°. What is the height of the mountain? The following steps will help you answer this question.
a) Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. Hint: Draw two right-triangles.
b) Select variable names for the mountain height (suggestion: y) and the woman's original distance from the mountain (suggestion: x) and label the picture.
c) Using the labelled picture and the tangent function, write two trigonometric equations relating the two selected variables.
d) Discover the height y of the mountain with first solving one equation for x and substituting the result into the other equation.