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Two ships are sailing in the sea on the two sides of a light house. The angles of elevation of the top of the light house as observed from the two ships are 30° and 45° respectively. If the light house is 100m high, the distance between the two ships is : (take √3 = 1.73 )
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- 173 metre
- 200 metre
- 273 metre
- 300 metre
Correct Option: C
AB = Light house = 100 metre
C and D are positions of ships.
Let,
BC = x metre and BD = y metre
∠ ACB = 45° and ∠ ADB = 30°
From ∆ ABC,
| tan 45° = | BC |
| ⇒ 1 = | ⇒ x = 100 metre | x |
From ∆ ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | y |
⇒ y = 100 √3 metre
= (100 × 1.73) metre
= 173 metre
∴ Required distance = x + y
= 100 + 173 = 273 metre
