Trig Applied Problems

Question

From a point P on level ground, the angle of elevation of the top of a tower is 25°40'. From a point 28.0 meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top is 58°50'. Approximate the height of the tower. (Round your answer to the nearest tenth.)

Answer 1

Draw and label of diagram!

B is at the base of the tower

S is at the point of the second sighting

T is at the top of the tower

tan 25°40' = TB / 28 + SB → TB = 28 sin 25ª40'

tan 58º 50' = TB / SB → TB = SB tan 58º50'

Solve for SB. Use that value to determine TB