A tower leans at an angle of about 847 degrees The figure sh

A tower leans at an angle of about 84.7 degrees. The figure shows that 152 feet from the base of the tower, the angle of elevation to the top is 53.6 degrees. Find the distance, to the nearest foot, from the base to the top of the tower. The distance is feet. (Round to the nearest integer as needed.)

Solution

angle A = 84.7

angle B = 53.6

AB = a = 152 feet

from fig, third angle

angle C = 180 - 84.7 - 53.6 = 41.7 degree

from sine formula:

sin C / 152 = sin 53.6 / b

sin 41.7 / 152 = sin 53.6 / b

b ( distance from base to top) = sin(53.6) *152 / sin(41.7)

b = 183.91 feet

= 184 feet