Question

A man was flying a kite. The string was 300 m long and formed an angle of 45° with the horizon. What was the height of the kite above the horizon?

a) 150 m
b) 212.1 m
c) 300 m
d) 424.3 m

Answer 1

Using the sine function and the given angle of 45°, the height of the kite above the horizon is calculated to be approximately 212.1 meters.

Step-by-step explanation:

The problem presents a scenario where a man is flying a kite with a string that is 300 m long and forms a 45° angle with the horizon. To find the height of the kite above the horizon, we can use trigonometric functions, specifically, the sine function, because the height of the kite will be opposite to the 45° angle while the string represents the hypotenuse of the right triangle formed.

To calculate the height (h) of the kite, we use the sine of 45° (which is √2/2 or approximately 0.7071) and multiply it by the length of the string (hypotenuse, H):
h = H × sin(45°) = 300 m × 0.7071 ≈ 212.1 m.