Question

use the diagram below to answer the following question(s).
it is believed that the best angle to fly a kite is 45°. if you fly a kite at this angle and let out 225 feet of string, approximately how high above the ground will the kite be?
100 feet
150 feet
200 feet
250 feet

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 45^{\circ}\), hypotenuse \(c = 225\) ft, and the height \(h\) (opposite side) is what we want to find. So, \(\sin45^{\circ}=\frac{h}{225}\).

Step2: Substitute the value of \(\sin45^{\circ}\)

Since \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\), then \(h = 225\times\sin45^{\circ}\).

Step3: Calculate \(h\)

\(h=225\times0.707 = 225\times\frac{\sqrt{2}}{2}\approx225\times0.707 = 159.075\approx160\) (close to 150 when considering approximation in the context of multiple - choice with possible rounding differences in the problem - making process).

Answer:

150 feet