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The length of a string between a kite an...

The length of a string between a kite and a point on the ground is `85` metres. If the string makes an angle `theta` with the ground level such that `tantheta=(15)/8,` how high is the kite? Assume that there is no slack in the string.

A

79 m

B

76 m

C

78 m

D

75 m

Text Solution

Verified by Experts

The correct Answer is:
D
Let OX be the horizontal ground and let A be the position of the kite. Let O be the position of the observer and OA be the string. Draw `AB_|_ OX`.
Then, `angleBOA = theta` and `tantheta = 15/8, OA = 85 m` and `angleOBA = 90^(@)`.
Let `AB = h` metres.
From height `DeltaOBA`, we have
`(AB)/(OA) = sintheta = 15/17 [ :' tan theta = (15)/(8) rArr sin =15/17]`
`rArr h/85= 15/17 rArr h = 15/17 xx 85 = 75`.
Hence the height of the kite from the ground is `75m`.
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