Question

nevaeh leans a 22-foot ladder against a wall so that it forms an angle of $64^{circ}$ with the ground. how high up the wall does the ladder reach? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\theta = 64^\circ$, hypotenuse = 22 ft, let height = $h$.
$\sin(64^\circ) = \frac{h}{22}$

Step3: Solve for height $h$

$h = 22 \times \sin(64^\circ)$
Calculate $\sin(64^\circ) \approx 0.8988$, so $h \approx 22 \times 0.8988$

Answer:

19.77 feet