Question

two ships are approaching a light house from opposite directions. the angle of depression of the two ships from the top of a light house are 30⁰and 45⁰. if the distance between the two ships is 100 meters, find the height of the light house​

Answer 1

Answer:

Let PQ be the light house whose height = h metre. Let A and B be the position of the ships on opposite sides of the lighthouse such that angle of depression for A and B are 30° and 45° respectively. Let AQ = x metre, QB = y metres. ∠PAQ = 30°, ∠PBQ = 45°. Required distance between the ships = AB = AQ + QB = x + y In rt. Δ PAQ, tan 30° = hxhx ⇒ 13√13 = hxhx ⇒ xx = h√3 In rt. Δ PBQ, tan 45° = hyhy ⇒ 1 = hyhy ⇒ y = h ∴ x + y = h√3 + h = h(√3 + 1)m.Read more on Sarthaks.com - https://www.sarthaks.com/1022262/from-light-house-angles-depression-ships-opposite-sides-the-lighthouse-are-observed-30