# The length of a string between a kite and a point on the ground is 90 metres. If the string makes an angle with the ground level such that tan =15/8, how high is the kite? Assume that there is no slack in the string.

Given: The length of a string between a kite and a point on the ground is 90 metres. If the string makes an angle with the ground level such that tan =15/8.

To find:  how high is the kite.

Solution:

Let the height of string = h (m)

tan θ = (given)

Since tanθ = perpendicular/base

So perpendicular= 15 and base=8

So we construct a right triangle ABC right angled at C such that

∠ABC=θ  and AC = Perpendicular = 15

BC = base = 8

By Pythagoras theorem,

AB2 = AC2 + BC2

⇒ AB2 = (15)2 + (8)2

⇒ AB2 = 225 + 64

⇒ AB2 = 289

⇒ AB = √289

⇒ AB = 17 Since Sin θ = perpendicular/hypotenuse

⇒ Sin θ = ..... (1)

In ∆ABC,

Sin θ = Sin θ = ...... (2) Equating (1) and (2) we get, = 17h = 90×15

⇒ h = ⇒h = 79.41 m.

Therefore length of string is 79.41 m.

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