-
The cliff of a mountain is 180 m high and the angles of depression of two ships on the either side of cliff are 30° and 60°. What is the distance between the two ships?
-
- 400 metre
- 400 √3 metre
- 415.68 metre
- 398.6 metre
Correct Option: C
AD = Cliff = 180 metre
∠ABD = 60°, ∠ACD = 30°
From ∆ABD,
| tan 60° = | BD |
| ⇒ √3 = | BD |
| ⇒BD = | = 60√3 metre | √3 |
From ∆ACD,
| tan 30° = | CD |
| ⇒ | = | √3 | CD |
⇒ CD = 100 √3 metre
∴ BC = BD + DC
= 60 √3 + 180 √3
= 240 √3 metre
= (240 × 1.732) metre
= 415.68 metre
