Answer:
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)
