-
The angles of depression of two ships from the top of a light house are 45° and 30° toward east. If the ships are 200m apart, the height of the light house is (Take √3 =1.73)
-
- 273 metre
- 270 metre
- 253 metre
- 263 metre
Correct Option: A
AB = Height of light-post = h metre
CD = 200 metre;
C and D ⇒ positions of ships
∠ACB = 45°; ∠ADB = 30°
In ∆ABC,
| tan 45° = | BC |
| ⇒ 1 = | ⇒ AB = BC = h metre | BC |
In ∆ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | h + 200 |
⇒ √3h = h + 200
⇒ √3h – h = 200
⇒ h (√3 - 1 ) = 200
| ⇒ h = | √3 - 1 |
| = | + 1) | (√3 - 1)(√3 + 1) |
| = | + 1) | 2 |
= 100 (1.73 + 1) metre
= 273 metre
