A woman measures the angle of elevation from her current location to a mountaintop to be 12.0°. After walking 1.10 km closer to the mountain on level ground, she measures the angle again and finds it to be 14.0°. What is the height of the mountain?

Answer 1

1. Draw a hor. line.
2. Draw a ver. line to the right-end of the hor. line and label it h for height.
3. From the left-end of the hor. line, draw a hypotenuse to the top of the ver. line. The angle it makes with the
hor. is 12o.

4. Draw a 2nd hyp. to the right of the first and label the distance between them X1 = 1.1 km. The remaining section
is X2.

Tan12 = h/(x1+x2) = h/(1.1+x2)
h = (1.1+x2)*Tan12

Tan14 = h/x2
h = x2*Tan14

x2*Tan14 = (1.1+x2)*Tan12
0.249x2 = 0.213x2 + 0.234
0.249x2-0.213x2 = 0.234
0.036x2 = 0.234
X2 = 6.5 km

h = X2*Tan14 = 6.5 * Tan14 = 1.62 km.