Question

A boy who is flying a kite lets out 300 feet of string which makes an angle of 60o with the ground. Assuming that the string is stretched taut, find, to the nearest foot, how high the kite is above ground.

Answer 1

Answer :

See the attachment for better understanding.

Given : Length of string (AC) = 300ft

To Find : Height of the kite from ground (AB)

$:\implies\sf\:sin60^{\circ}=\dfrac{AB}{AC}$

$:\implies\sf\:\dfrac{\sqrt{3}}{2}=\dfrac{H}{300}$

$:\implies\sf\:H=\dfrac{300\sqrt{3}}{2}$

$:\implies\sf\:H=150\sqrt{3}$

$:\implies\:\boxed{\bf{\red{H\approx 260\:feet}}}$

Hope it helps !

Answer 2

The kite is 260 ft. above ground.

What is right triangle?

"It is a triangle whose one of the angle is 90"

What is sine of the angle?

For right triangle the sine of the angle 'x' is,

sin(x) = opposite side of angle x / hypotenuse

For given example,

Consider the diagram given below.

KL represents the string length.

So, KL = 300 ft.

A string makes an angle of 60° with the ground.

This means, ∠KLM = 60°

Let, 'h' represents the height of of the kite above the ground.

For a right triangle KLM,

⇒ sin(KLM) = KM/KL

⇒ sin(60°) = h/300

⇒ h = sin(60°) × 300

⇒ h = 259.8 ft.

⇒ h ≈ 260 ft.

Therefore, the kite is 260 ft. above ground.

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