Question

question 3 (essay worth 10 points)
(05.03 hc)
caitlin is flying a kite. the angle of elevation formed by the kite string and the ground is 40°, and the kite string forms a straight segment that is 100 feet long.
explain how to find the distance between the ground and the kite. include a description of the triangle you drew to help you solve, including the variables and measurements you assigned to each side and angle. round your answer to the
nearest foot.

Explanation:

Step1: Identify the triangle type

We have a right - triangle. Let the distance between the ground and the kite be \(h\) (opposite side), the kite string length \(l = 100\) feet (hypotenuse), and the angle of elevation \(\theta=40^{\circ}\).

Step2: Use the sine function

The sine of an angle in a right - triangle is given by \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(40^{\circ})=\frac{h}{100}\).

Step3: Solve for \(h\)

$$h = 100\times\sin(40^{\circ})$$

Using a calculator, \(\sin(40^{\circ})\approx0.6428\). Then \(h = 100\times0.6428 = 64.28\approx64\) feet.

Answer:

The distance between the ground and the kite is approximately \(64\) feet.