Question

A 125-foot line is attached to a kite. When the kite has pulled the line taut, the angle of elevation to the kite is approximately 65°. Approximate the height of the kite to the nearest foot.

a) 95 feet
b) 109 feet
c) 120 feet
d) 130 feet

Answer 1

By using the sine function of the given 65° angle of elevation and the length of the line, the height of the kite is calculated to be approximately 113 feet. As this answer is not provided in the options, there may be an error in the given information or the multiple-choice answers.

Step-by-step explanation:

To approximate the height of the kite to the nearest foot, we can apply trigonometry, specifically the sine function, which relates an angle in a right triangle to the ratio of the length of the opposite side to the hypotenuse. If we let 'h' represent the height of the kite and use the given 125-foot line (the hypotenuse) and the 65° angle of elevation, we have:

sin(65°) = h / 125

Multiplying both sides by 125 yields:

125 * sin(65°) = h

Using a calculator to find the sine of 65°:

h ≈ 125 * 0.9063

h ≈ 113.29 feet

Since we need to approximate to the nearest foot, the height of the kite is about 113 feet, which is not an option provided. Please double-check the angle of elevation or the options listed for possible errors.