Question

1. madeline leans a 30 - foot ladder against a wall so that it forms an angle of 72° 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 the trig - function

We have a right - triangle where the length of the hypotenuse (the ladder) is 30 feet and the angle between the ladder and the ground is 72°. We want to find the adjacent side (the horizontal distance $x$) to the given angle. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos\theta=\frac{x}{30}$, where $\theta = 72^{\circ}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos72^{\circ}=\frac{x}{30}$ by 30. So $x = 30\times\cos72^{\circ}$.
We know that $\cos72^{\circ}\approx0.3090$. Then $x = 30\times0.3090=9.27$.

Answer:

9.27 feet