Let's denote the height of the pole as x meters.
From the foot of the tower, the woman observes the top of the pole at an angle of elevation of 30 degrees. This forms a right triangle with the height of the tower (30m) and the height of the pole.
Therefore, in this right triangle:
tan(30) = 30/x
x = 30 / tan(30)
x ≈ 51.96 meters
From the top of the tower, the woman observes the top of the pole at an angle of depression of 25 degrees. This also forms a right triangle with the height of the tower (30m) and the height of the pole.
Therefore, in this right triangle:
tan(25) = 30 + x / x
x = (30 + x) * tan(25)
x = 43.72 meters
Therefore, the height of the pole is approximately 43.7 meters.
From the foot of a tower, 30m high, a woman observes the top of a pole at an angle of elevation of 30 degrees, from the top of the tower, she observes the top of the pole at an angle of depression of 25 degrees, if the pole and the tower are on the same horizontal level: find, correct to one decimal place the height of the pole
1 answer