Question

From a point on the ground, the angle of elevation of the top of a tower is 30°. After walking 20 m towards the tower, the angle of elevation becomes 45°. Find the height of the tower. (Use √3 = 1.732.)

Solution

1. Let the height be h. From the second point, tan 45° = h / d, so the distance is d = h.
2. From the first point, tan 30° = h / (d + 20), so d + 20 = h / tan 30° = h√3.
3. Substitute d = h: h + 20 = h√3, so h(√3 - 1) = 20.
4. h = 20 / (√3 - 1) = 20(√3 + 1) / 2 = 10(√3 + 1) = 10 x 2.732 = 27.32 m.
5. The height of the tower is about 27.3 m.