Question

1. a kite is flying attached to a string that is 150 ft long. the string is tied to the ground and is flying at an angle of 45°. how high is the kite flying?

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem where the string is the hypotenuse (\(c = 150\) ft) and the height of the kite is the opposite side (\(h\)) to the angle of elevation (\(\theta=45^{\circ}\)). We use the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Apply the sine formula

We know that \(\sin(45^{\circ})=\frac{h}{150}\). Since \(\sin(45^{\circ})=\frac{\sqrt{2}}{2}\approx0.7071\), we can solve for \(h\):
\(h = 150\times\sin(45^{\circ})\)
\(h=150\times\frac{\sqrt{2}}{2}\)
\(h = 75\sqrt{2}\approx75\times1.4142 = 106.065\) ft

Answer:

The kite is flying at a height of \(75\sqrt{2}\) ft (or approximately \(106.07\) ft)