-
From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff.
(Take √3 = 1.732)
-
- 10 (√3 + 2) m
- 10 (√3 + 1) m
- 10 √3 m
- 7.32 m
Correct Option: D
AC = Flag
AB = building = 10 metre
∠ APB = 30°; ∠ CPB = 45°
In ∆ APB,
| tan 30° = | PB |
| ⇒ | = | |||
| √3 | PB |
⇒ PB = 10 √3 metre
In ∆ PBC,
| tan 45° = | PB |
| ⇒ 1 = | PB |
⇒ PB = AB + AC
⇒ 10 √3 = 10 + AC
⇒ AC = 10 √3 – 10
= 10 ( √3 –1) metre
= 10 (1.732 – 1) metre
= 10 × 0. 732 = 7.32 metre
