Two points A and B are on the ground and on opposite sides of a tower. A is closer to the foot of the tower by 42 m than B. If the angle of elevation of the top of the tower, as observed from A and B are 60° and 45°, respectively, then the height of the tower is closest to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 99.4 m
| Understanding | Application |
| Tricks |  |
| Now |
tan60 = OC/AO √3 = OC/x OC = x√3 .....i) & tan45 = OC/OB 1 = OC/x + 42 OC = x + 42 ....ii) |
| From eqi) and eqii) |
x√3 = x + 42 ⇒ x(√3 - 1) = 42 ⇒ x = 42/(√3 - 1) × (√3 + 1)(√3 + 1) ⇒ 42(√3 + 1)/2 ⇒ 21(√3 + 1) |
| Hence |
OC = height = 21(√3 + 1)√3 = 63 + 21√3 = 63 + 36.33 = 99.33 = 99.4 |