Question

A kite with a string 80 feet long makes an angle of elevation of 40° with the ground, assuming the string is straight, how high is the kite? Round your answer to the nearest foot. Do not include units.

Answer 1

The diagram of the kite is shown below

To find the perpendicular height of the kite from the ground, we use the trigonometry ratio for sin(x).

The reason for using the sine ratio is because we have the hypotenuse, 80 feet, and the angle, 40° and we are looking for the length of the side opposite the angle.

$sin(x)= \frac{opp}{hyp}$
$sin(40)= \frac{x}{80}$
$80sin(40)=x$
$x=51.42$ rounded to two decimal place

Perpendicular height of the kite from the ground is 51.42 feet