Heights and Distances Practice Test 1

Question : 25 of 40

Marks: +1, -0

The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance a towards the foot of the tower the angle of elevation is found to be β. The height of the tower is:

${a\sinα\sinβ}/{\sin(β-α)}$
${a\sinα\sinβ}/{\sin(α-β)}$
${a\sin( β-α)}/{ \sinα\sinβ}$
${a\sin( α-β)}/{ \sinα\sinβ}$

Validate

Solution:

Let OP be the tower of height h (say) and A and B be the two positions on the horizontal line through O, such that
∠ OAP = α, ∠ OBP = β and OB = x
In ΔOBP, OB = x = h cot β, and
in ΔOAP, OA = a + x = h cot α
∴ a = h (cot α – cot β)

⇒ h ={ a \sin α \sin β}/{\sin (β - α)}

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