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Calculating Heights and Distances

Question

A balloon is observed simultaneously from three points A B and C, on a straight road directly under it. The angular elevation at B is twice of what it is at A and the angular elevation at C is thrice of what it is at A. If the distance between A and B is 200 meters and the distance between B and C is 100 meters, then find the height of the balloon.
$50$ m
$50 \sqrt{3}$ m
$150 \sqrt{3}$ m
$100 \sqrt{3}$ m

A

50

m

B

50 \sqrt{3}

m

C

150 \sqrt{3}

m

D

100 \sqrt{3}

m

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