Two ships are sailing in the sea on the two sides of a lighthouse, the angle of depression

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Let height of the pedestal BD be h metres, and angle of elevation of C and D at a point A on the ground be 60° and 45° respectively.It is also given that the height of the statue CD be 1.6 mi.e.,    ∠CAB = 60°,∠DAB = 45° and CD = 1.6mIn right triangle ABD, we have

Hence, the height of pedestal 

Let A and B the position of the first ship and the second ship

Distance = `200((sqrt(3) + 1)/sqrt(3))`m

Let the height of the lighthouse CD be h

`sqrt(3) = "h"/"AD"`

 ∴ AD = `"h"/sqrt(3`  ...(1)

In the right ∆BCD

tan 45° = `"DC"/"BD"`

1 = `"h"/"BD"`

∴ BD = h

Distance between the two ships = AD + BD

`200((sqrt(3) + 1)/sqrt3) = "h"/sqrt3 + "h"`

⇒ `200 (sqrt(3) + 1) = "h" + sqrt(3)"h"`

`200(sqrt(3) + 1) = "h"(1 + sqrt(3))`

⇒ h = `(200(sqrt(3) + 1))/((1 + sqrt(3))`

h = 200

Height of the light house = 200 m