Question

riley leans a 16 - foot ladder against a wall so that it forms an angle of 74° 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: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 74^{\circ}\), the hypotenuse is the length of the ladder \(c = 16\) feet, and the adjacent side is \(x\) (the horizontal distance we want to find). So, \(\cos(74^{\circ})=\frac{x}{16}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(74^{\circ})=\frac{x}{16}\) by \(16\). We get \(x = 16\times\cos(74^{\circ})\).
Since \(\cos(74^{\circ})\approx0.2756\), then \(x = 16\times0.2756\).
\(x=4.4096\)

Answer:

\(4.41\) feet