Question

a ladder leans against a wall. the bottom of the ladder is 5 feet from the base of the wall, and the angle it makes with the ground is 60 degrees. how long is the ladder?

Explanation:

Step1: Identify trigonometric ratio

We use cosine, since $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta=60^\circ$, adjacent side = 5 ft, hypotenuse = ladder length $L$.

Step2: Substitute values into formula

$\cos(60^\circ) = \frac{5}{L}$
We know $\cos(60^\circ) = \frac{1}{2}$, so:
$\frac{1}{2} = \frac{5}{L}$

Step3: Solve for $L$

Rearrange to isolate $L$:
$L = 5 \times 2$

Answer:

10 feet