The angle of elevation of a cloud from a point 10 meters above the surface of a lake is 30 o and the angle of depression of its reflection from that point is 60 o . Then the height of the cloud above the lake is

Step-by-step solution

Let C be the cloud, D its reflection and P B is the surface of the lake Then, P C = P D = H , Q A = H - 10 cot ⁡ 30 o = H + 10 cot ⁡ 60 o H = 10 cot ⁡ 3 0 o + cot ⁡ 6 0 o cot ⁡ 3 0 o - cot ⁡ 6 0 o = 10 sin ⁡ 9 0 o / s i n 3 0 o = 20 meters