Richard is flying a kite at an angle elevation of 52 degrees. he is 5 ft tall. If richard is standing 100 ft from the point on the ground directly below the kite, compute the length of the kite string.
cos52 = X/L = 100/L
L = 100/cos52
To compute the length of the kite string, we can use the concept of trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation to the ratio of the opposite side to the adjacent side in a right triangle.
Here's how you can calculate the length of the kite string using the given information:
1. Convert the angle of elevation from degrees to radians. The formula to convert degrees to radians is: radians = degrees * (π/180). In this case, we have 52 degrees, so the angle in radians would be:
radians = 52 * (π/180) ≈ 0.9076 radians.
2. Now we can set up the trigonometric relationship using tangent: tan(angle) = opposite / adjacent.
In this case, the opposite side is the height of Richard (5 ft), and the adjacent side is the distance between Richard and the point on the ground directly below the kite (100 ft). So we have:
tan(0.9076) = 5 / 100.
3. Now, isolate the length of the kite string by multiplying both sides of the equation by 100:
100 * tan(0.9076) = 5.
4. Calculate the length of the kite string:
length of kite string = 100 * tan(0.9076).
Using a calculator, we find that the length of the kite string is approximately 89.6 feet.