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
In right triangle ABC, we have
Comparing (i) and (ii), we get
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
In the right ∆ACD, tan 60° = `"CD"/"AD"`
`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