Question

micaela leans a 18-foot ladder against a wall so that it forms an angle of $78^\circ$ 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 cosine relationship

The horizontal distance $x$ is the adjacent side to the $78^\circ$ angle, and the ladder (18 ft) is the hypotenuse. Use $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(78^\circ)=\frac{x}{18}$

Step2: Solve for $x$

Rearrange the formula to isolate $x$.
$x=18\times\cos(78^\circ)$

Step3: Calculate the value

Compute $\cos(78^\circ)\approx0.2079$, then multiply by 18.
$x\approx18\times0.2079=3.7422$

Answer:

3.74 feet