In travelling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 4.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9.5°.

Answer 1

X1 = Distance from closest point to bottom of mountain.

X1+13 = Distance from farthest point to bottom of mountain.

Tan9.5 = h/X1, h = X1*Tan9.5.

Tan4.5 = h/(X1+13), (X1+13)*Tan4.5.

h = X1*Tan9.5 = (X1+13)*Tan4.5
X1 = 0.507(X1+13) = 0.507X1+6.59.
X1-0.501X1 = 6.59.
0.5X1 = 6.59.
X1 = 13.2 Mi.

Tan9.5 = h/13.2
h = 13.2*Tan9.5 = 2.21 Miles.