Question

kiran is flying a kite. he gets tired, so he stakes the kite into the ground. the kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. how high is the kite? type your answer in the box. feet

Explanation:

Step1: Identify the trigonometric relation

We have a right triangle where the hypotenuse (length of the string) is 18 feet, the angle with the ground is \(30^\circ\), and we need to find the opposite side (height of the kite), so we use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute values into the formula

Here, \(\theta = 30^\circ\), hypotenuse \(= 18\) ft. So \(\sin(30^\circ)=\frac{\text{height}}{18}\). We know that \(\sin(30^\circ)=\frac{1}{2}\), so \(\frac{1}{2}=\frac{\text{height}}{18}\).

Step3: Solve for height

Multiply both sides by 18: \(\text{height}=18\times\frac{1}{2}=9\) feet.

Answer:

9