Question
It is believed that the best angle to fly a kite is 45 degrees. If you fly a kite and let out 190 feet of string, approximately how high above the ground will the kite be?
Answers
GPT-4o mini
To find the height of the kite above the ground when flown at a 45-degree angle with 190 feet of string, we can use trigonometry.
At a 45-degree angle, the height (h) and the horizontal distance (d) from the flyer to the kite are equal. Since the total length of the string is the hypotenuse of a right triangle, we can use the sine function:
\[
h = L \cdot \sin(\theta)
\]
where \( L \) is the length of the string (190 feet) and \( \theta \) is the angle (45 degrees).
The sine of 45 degrees is \( \frac{\sqrt{2}}{2} \). Therefore:
\[
h = 190 \cdot \sin(45^\circ) = 190 \cdot \frac{\sqrt{2}}{2}
\]
Calculating \( \sin(45^\circ) \):
\[
h = 190 \cdot \frac{\sqrt{2}}{2} \approx 190 \cdot 0.7071 \approx 134.16
\]
Thus, the kite will be approximately 134.16 feet above the ground.
So the answer is:
**Approximately 134.16 feet**.
At a 45-degree angle, the height (h) and the horizontal distance (d) from the flyer to the kite are equal. Since the total length of the string is the hypotenuse of a right triangle, we can use the sine function:
\[
h = L \cdot \sin(\theta)
\]
where \( L \) is the length of the string (190 feet) and \( \theta \) is the angle (45 degrees).
The sine of 45 degrees is \( \frac{\sqrt{2}}{2} \). Therefore:
\[
h = 190 \cdot \sin(45^\circ) = 190 \cdot \frac{\sqrt{2}}{2}
\]
Calculating \( \sin(45^\circ) \):
\[
h = 190 \cdot \frac{\sqrt{2}}{2} \approx 190 \cdot 0.7071 \approx 134.16
\]
Thus, the kite will be approximately 134.16 feet above the ground.
So the answer is:
**Approximately 134.16 feet**.