Question

An observer in a lighthouse observes two ships on the same side of the lighthouse, and in the same straight line with the base of the lighthouse. The angles of depression of the ships approaching it are 30° and 60°. If the height of the lighthouse is 150 m, find the distance between the ships

Answer 1

Answer: The distance between the two ship is 173.205m

Step-by-step explanation:

Answer 2

An observer in a lighthouse observes two ships on the same side of the lighthouse, and in the same straight line with the base of the lighthouse. The angles of depression of the ships approaching it are 30° and 60°. If the height of the lighthouse is 150 m

Height of the tower(AB)=150m

Distance between two ships (CD) = x m

BC = y m

i ) In ∆ABD , <ABC =90°

tan 30° = AB/BD

=> 1/√3 = 150/(x+y)

=> x+y = 150√3

x = 150√3 - y ----(1)

ii) In ∆ABC, <ABC = 90°

tan60° = AB/BC

=> √3 = 150/y

=> y = 150/√3

= (150√3)/(√3×√3)

= (150√3)/3

= 50√3 -----(2)

Substitute y =50√3 in equation (1) , we get

=> x = 150√3 - 50√3

=> x = 100√3 m

Therefore,

Distance between two ships = x = 100√3 m

=> x = 100×1.732

=> x ≈ 173.2 m

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