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Q.

If the angles of elevation of the top of the candle from two coins distant ‘a' cm and ‘b’ cm (a>b) from its base and in the same straight line from it are 30˚ and 60˚, then find the height of the candle.

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a

ab cm

b

a b cm

c

a b cm

d

b a cm

answer is B.

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Detailed Solution

Given that, the angles of elevation of the top of the candle from two coins distant ‘a' cm and ‘b’ cm (a>b) from its base and in the same straight line from it are 30˚ and 60˚.
Let the candle be AB and the coins C, D are at a distance of ‘a’ cm and ‘b’ cm respectively from base B.
Consider the following figure, based on the given information.
Question Image

Question Image

Let us assume,

BD=a and BC = b

.
We can observe that, in

Δ A B D

tan 30 ° = h a

.
But,

13 = h / a h = a 3 … … .. [1]

Let us find the height of the triangle.
In

Δ A B C

,

tan C = C D B C tan 60 ° = h b 3 = h b h = b 3 … … … . [2]

Multiplying (1) and (2), we get,

h × h = a 3 × b 3 h 2 = a b h = a b cm

The height of the candle

h = a b cm

The correct option is (2).

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