Question

arianna leans a 28-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 tenth of a foot if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=64^\circ$, opposite side is $x$, hypotenuse $=28$.

Step2: Rearrange to solve for $x$

$x = 28 \times \sin(64^\circ)$

Step3: Calculate the value

First find $\sin(64^\circ) \approx 0.8988$, then $x \approx 28 \times 0.8988$
$x \approx 25.1664$

Step4: Round to nearest tenth

$x \approx 25.2$

Answer:

25.2 feet