Question

Huang is standing 14 meters from the base of a kite. The kite string makes a 67° angle with the ground. Find x, the length of the kite string. Round to the nearest hundredth.

Answer 1

To find the length of the kite string, we can use trigonometry.

First, we will find the height of the kite by using the sine function:
sin(67°) = opposite/hypotenuse
sin(67°) = height/14
height = 14 * sin(67°)
height ≈ 13.03 meters

Now we can find the length of the kite string using the Pythagorean theorem:
x² = 14² + 13.03²
x² = 196 + 169.54
x² ≈ 365.54
x ≈ √365.54
x ≈ 19.12 meters

Therefore, the length of the kite string is approximately 19.12 meters.