## points P and Q lie 240 m apart in line with and on opposite sides of a communications tower. the angles of elevation to the top of the tower

Question

points P and Q lie 240 m apart in line with and on opposite sides of a communications tower. the angles of elevation to the top of the tower from P and Q are 50 and 45 degrees, respectively. determine the height of the tower to the nearest tenth of a meter

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2 weeks 2021-09-13T16:14:07+00:00 1 Answer 0

The height of the tower is 130.5m

Step-by-step explanation:

In the question, we are given the following values:

The angles of elevation to the top of the tower from P = 50°

The angles of elevation to the top of the tower from Q = 45°

The angles of elevation to the top of the tower from P = 50°

Hence,cot P = 1/ tan(50°)

The angles of elevation to the top of the tower from Q = 45°

Hence, tan 45° = 1

In the question,we are told Points P and Q lie 240 m apart in line with and on opposite sides of a communications tower.

Therefore,

PQ = height of the tower( tan Q + 1/tan P)

240m = height of the tower( tan 45° + 1/ tan 50°)

240m = h(1 + 1/tan 50°)

h = (240 m)/(1 + 1/tan (50°))

h = 130.49863962 meters

Therefore, the height of the tower to the nearest tenth of a meter is 130.5 meters(m)