From the top of the lamp post of height x meters to objects on the ground on the same side of it ( and in line with the foot of the lamp post) all observed at angles of depression of 30° and 60° respectively. The distance between the objects is 32√3m. The value of x is?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 48
| Application |
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Let RQ is a lamp post of x metres and two objects are placed at P and S respectively such that PS = 32√3 Let SQ = y metres
In triangle PQR Tan 30 = (RQ/PQ) = RQ/(PS + SQ) =x/32√3 + y 1/√3 = x/32√3 + y............(1) In triangle SQR tan 60 = x/y = √3y = x y = x/√3........(2) Put value from (2) in (1) 1/√3 = x/(32√3+x/√3) 1/√3 = √3x/96 + x 3x = 96 + x x = 48 metres |
