Question

A SURVEYOR STANDING W25 S OF TOWER MEASURES THE angle of elevation of the top of the tower as 46,5 degrees. From a position E23 S from the tower the elevation of the top is 37,728 degrees. The distance between the two points is 75m, find the height if the tower

Answer 1

Let's denote the height of the tower as h.

From the first position, the surveyor is standing W25 S of the tower and measures an angle of elevation of 46.5 degrees. This can be represented as a right-angled triangle with the tower as the vertical side (h) and the horizontal distance from the surveyor to the base of the tower as the base (25m). We can use trigonometry to find the height of the tower:

tan(46.5) = h/25
h = 25 * tan(46.5)
h ≈ 25 * 1.0635
h ≈ 26.59m

From the second position, the surveyor is standing E23 S from the tower and measures an angle of elevation of 37.728 degrees. This can be represented as another right-angled triangle with the tower as the vertical side (h) and the horizontal distance from the surveyor to the base of the tower as the base (75m). We can use trigonometry to find the height of the tower:

tan(37.728) = h/75
h = 75 * tan(37.728)
h ≈ 75 * 0.766
h ≈ 57.45m

Since the height of the tower should be the same regardless of the position of the surveyor, we can average these two values to find the height of the tower:

Average height = (26.59 + 57.45) / 2
Average height ≈ 83.04 / 2
Average height ≈ 41.52m

Therefore, the height of the tower is approximately 41.52 meters.