Question

a surveyor finds that from Point A on the ground the angle of elevation to the top of a mountin is 23 degrees. when he is at point B that is 1/4 closer to the base of the mountain the angle of elevation is 43 degrees. how high is the moutnain? One mile =5280 feet. (Assume that thr base of the mountain and the two observation points are on the same line.)Give answer to the nearest foot.

Answer 1

tan23 = Y/X,
Y = Xtan23,

tan43 = Y/(X-.25).
Y = (X-0.25)tan43.

y = Xtan23 = (X-0.25)tan43,
Xtan23 = (X-0.25)tan43,
Xtan23 = Xtan43-0.25tan43,
0.4245X = 0.9325X-0.2331,
0.4245X-0.9325X = -0.2331,
-0.508X = -0.2331,
X = 0.4589 Miles.

y = 0.4589tan23 = 0.1948 miles.

Y = 0.1948mi * 5280ft/mi = 1029 Ft.
= Height of mountain.