Question

From a light house the angles of depression of two ships on opposite side of the light house are observed to be 30° and 45°. If the height of light house be 300 metres, find the distance between the ships if the line joining them passes through the foot of the light house.

Answer 1

Let HK be the light house 300 m in height. Let A and B be the two ships, such that angles of depression LHA and MHB are respectively 30° and 45°. It follows that ∠HAK = 30° and ∠HBK = 45°. 

Also, ∠KHB = 45°, and therefore, KB = HK = 300 m 

Also, ∠AHK = 60°

From ΔHAK, we get, \(\frac{AK}{HK}\) = tan 60° 

∴ AK = HK × tan 60° = 300 × 1.7321 = 519.63 m 

∴ AB = AK + KB = 519.63 m + 300 m = 819.63 m.