Question

An observer on the top of a cliff, 150 m above the sea level, observes the angles of
depression of the two ships to be 45 ° and 30 ° respectively. If the ships are on the
opposite sides of the cliff. Find the distance between the ships.
Only Valid answers pls

Answer 1

Answer:

The distance between ships  14.64 m if on the same side of cliff  & 54.64 m if on the opposite sides of cliff.

Step-by-step explanation:

Tan α = Height of cliff/ Horizontal Distance from cliff

Tan 45  = 20/Distance of Ship from Cliff

=> 1  = 20/Distance of Ship from Cliff

=> Distance of Ship from Cliff = 20

Tan 30  = 20/Distance of Ship from Cliff

=> 1/√3  = 20/Distance of Ship from Cliff

=> Distance of Ship from Cliff = 20√3

(i) on the same side of cliff

Distance between Ships  =  20√3 - 20  = 20 (√3 - 1) m  = 14.64 m

(ii) on the opposite sides of cliff

Distance between Ships  =  20√3 + 20  = 20 (√3 + 1) m  = 54.64 m

Answer 2

The Answer is in Attachment

Hope it Help you