Question

question
makayla leans a 18-foot ladder against a wall so that it forms an angle of $64^{\circ}$ with the ground.
whats the horizontal distance between the base of the ladder and the bottom of the wall? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use cosine, since $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where the adjacent side is the horizontal distance we need, the hypotenuse is the ladder length, and $\theta = 64^\circ$.

Step2: Plug in known values

Let $x$ = horizontal distance.
$\cos(64^\circ) = \frac{x}{18}$

Step3: Solve for $x$

$x = 18 \times \cos(64^\circ)$
Calculate $\cos(64^\circ) \approx 0.4384$, so $x \approx 18 \times 0.4384$
$x \approx 7.9$

Answer:

7.9 feet