Question

skylar leans a 24-foot ladder against a wall so that it forms an angle of $60^\circ$ 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 hundredth of a foot if necessary.

Explanation:

Step1: Identify trigonometric ratio

The horizontal distance $x$ is adjacent to the $60^\circ$ angle, and the ladder (24 ft) is the hypotenuse. Use cosine:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(60^\circ) = \frac{x}{24}$

Step3: Solve for $x$

$x = 24 \times \cos(60^\circ)$
Since $\cos(60^\circ) = 0.5$,
$x = 24 \times 0.5 = 12$

Answer:

12 feet