Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Given

• Height of lighthouse, H = 100 m
• Angles of elevation from the two ships: 30° and 45°
• Ships are on opposite sides of the lighthouse

Step 1: Horizontal distance of ship with 30°
\tan 30^\u00b0 = 𝐻 𝑑 1 d 1 ​ H ​ ⇒ 1 3 3 ​ 1 ​ = 100 𝑑 1 d 1 ​ 100 ​ d 1 1 ​ = 100 3 3 ​ m

Step 2: Horizontal distance of ship with 45°
\tan 45^\u00b0 = 𝐻 𝑑 2 d 2 ​ H ​ = 1 ⇒ d 2 2 ​ = 100 m

Step 3: Distance between ships
Opposite sides ⇒ total separation = d 1 1 ​ + d 2 2 ​ = 100 3 3 ​ + 100 = 100(\u221A3 + 1) m