As observed from the top of a lighthouse 45m high above the sea-level, the angle of depression of a ship, sailing directly towards it, changes from 30º to 45º. The distance traveled by ship during the period of observation is:
(Your answer should be correct to one decimal place.)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 32.9 m
| Understanding | Application |
| Tricks |
According to the question, we have drawn the figure
|
| Now |
tan45 = AB/BC ⇒ 1 = 45/x ⇒ x = 45 ......i) & tan30 = AB/BD ⇒ 1/√3 = 45/(x + y) ⇒ 1/√3 = 45/(45 + y) ⇒ 45 + y = 45√3 ⇒ y = 45√3 - 45 ⇒ y = 45(√3 - 1) ⇒ y = 45(1.73 - 1) |
| Hence |
⇒ y = 45 × 0.73 ⇒ y = 32.85 ⇒ y = 32.9 |
