Question

A kite flying in the air has a 12ft line attached to it. It's line is pulled taut and casts an 8ft shadow. Find the height of the kite.If necessary round to the nearest tenth

Answer 1

The height of the kite is 8.9 feet.

Explanation:

We have drawn diagram for your reference.

Given:

Distance of kite from the line = 12 ft.

According to diagram;

AC = 12 ft

Distance of the shadow of the line taut = 8 ft

According to diagram;

BC = 8 ft

We need to find the height of the kite AB.

Solution:

Let us consider the scenario to be a right angled triangle with right angle at B.

So we will use Pythagoras theorem.

"In a right angle triangle square of sum of 2 sides is equal to square of the third side."

framing in equation form we get;

`AB^2+BC^2=AC^2\\\\AB^2=AC^2-BC^2`

Substituting the given values we get;

`AB^2= 12^2-8^2\\\\AB^2= 144-64\\\\AB^2 = 80`

Taking Square root on both side we get;

`√(AB^2)=√(80)\\\\AB=8.944 ft`

rounding to nearest tenth we get;

`AB =8.9\ ft`

Hence The height of the kite is 8.9 feet.