Question

A man standing on the deck of a ship, which is 8m above water level. He observes the angle of elevation of the top of a hill as 60degree and the angle of depression of the base of the hill is 30degree. Find the distance of the hill from the ship and height of the hill.

Answer 1

Height of hill=32m

Distance from ship to hill=8√3m

inebc tan30_Height of hill=32m

Distance from ship to hill=8√3m

Answer 2

SOLUTION ☺️

Let x be the distance of hill from man and h+ 8 be the height of hill which is to be calculated.

In right Angled ∆ ACB

=) tan 60°= h/x

=) √3 = h/x

=) h= √3. x..........(1)

Also, In right Angled ∆ BCD

=) tan 30° = 8/x

=) 1/√3= 8/x

=) x= 8√3.............(2)

Using (1) &(2), we get

=) h= √3 × 8√3

=) 8×3

=) 24metres

Hence required height of the hill = h+8

=) 24+8= 32

Distance of the ship from the hill

=) x= 8√3 m

hope it helps ✔️