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Assume the distance of the earth from the moon to be $38, 400$ km and the angle subtended by the moon at the eye of a person on the earth to be $31 ’$ , find the diameter of the moon.

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3464 \frac{8}{63}

3564 \frac{8}{63}

346 \frac{8}{63}

3664 \frac{8}{63}

answer is A.

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Detailed Solution

It is given that the distance of the earth from the moon is

38, 400

km. The angle subtended by the moon at the eye of a person on the earth is

31'

.
According to the given data the figure has been drawn below.
Question Image

Let

PQ

be the diameter of the moon and

A

be the observer.
Converting

∠ PAQ = 31'

in radian,

\Rightarrow \frac{31}{60} \times \frac{π}{180}

rad.
We know,

θ = \frac{l}{r}

⟹ θ \times r = l

⟹ l = \frac{31}{60} \times \frac{π}{180} \times r

∴

PQ = \frac{31}{60} \times \frac{22}{7 \times 180} \times 38, 4000

⟹ PQ = 3464 \frac{8}{63}

km
So the diameter of the moon is

3464 \frac{8}{63}

km.
So the correct option is 1.

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