Question

a 25 - foot long ladder is propped against a wall at an angle of 18° with the wall. how high up the wall does the ladder reach? round the answer to the nearest tenth of a foot.
13.8 ft
23.8 ft
26.3 ft
80.9 ft

Explanation:

Step1: Define cosine relationship

We use the cosine function, where $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side is the height up the wall ($h$), hypotenuse is ladder length (25 ft), $\theta=18^\circ$.
$\cos(18^\circ) = \frac{h}{25}$

Step2: Solve for height $h$

Rearrange to isolate $h$: multiply both sides by 25.
$h = 25 \times \cos(18^\circ)$

Step3: Calculate and round

Compute $\cos(18^\circ) \approx 0.9511$, then $h \approx 25 \times 0.9511 = 23.7775$, rounded to nearest tenth is 23.8.

Answer:

B. 23.8 ft