Question

piper leans a 20 - foot ladder against a wall so that it forms an angle of 80° 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: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 80^{\circ}\), hypotenuse \(= 20\) and adjacent side is \(x\). So, \(\cos(80^{\circ})=\frac{x}{20}\).

Step2: Solve for \(x\)

Multiply both sides by \(20\): \(x = 20\times\cos(80^{\circ})\).
Using a calculator, \(\cos(80^{\circ})\approx0.1736\). Then \(x = 20\times0.1736 = 3.472\).

Answer:

\(3.5\) feet (rounded to the nearest tenth)