Question

huang is standing 14 meters from the base of a kite. the kite string makes a $67^{\circ}$ angle with the ground. find $x$, the length of the kite string. round to the nearest hundredth. (1 point)$\bigcirc$ $x = 35.83$ m$\bigcirc$ $x = 69.05$ m$\bigcirc$ $x = 5.47$ m$\bigcirc$ $x = 15.21$ m

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle where the adjacent side to the 67° angle is 14 m, and \(x\) (kite string) is the hypotenuse. Use cosine:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(67^\circ) = \frac{14}{x}$

Step3: Solve for \(x\)

Rearrange to isolate \(x\):
$x = \frac{14}{\cos(67^\circ)}$

Step4: Calculate the value

Use $\cos(67^\circ) \approx 0.3907$:
$x \approx \frac{14}{0.3907} \approx 35.83$

Answer:

$x = 35.83$ m