Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Question: Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
[A].
173 m
200 m
273 m
300 m
[A].
[B].
[C].
[D].
Answer: Option C
Explanation:
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, ACB = 30° and ADB = 45°.
| AB | = tan 30° = | 1 | AC = AB x 3 = 1003 m. |
| AC | 3 |
| AB | = tan 45° = 1 AD = AB = 100 m. |
| AD |
| CD = (AC + AD) | = (1003 + 100) m |
| = 100(3 + 1) | |
| = (100 x 2.73) m | |
| = 273 m. |