Question

jackson leans a 18 - foot ladder against a wall so that it forms an angle of 69° with the gro whats the horizontal distance between the base of the ladder and the bottom of the wall? 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, \(\theta = 69^{\circ}\), the hypotenuse \(c = 18\) and the adjacent side is \(x\). So, \(\cos(69^{\circ})=\frac{x}{18}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(69^{\circ})=\frac{x}{18}\) by \(18\). Then \(x = 18\times\cos(69^{\circ})\).
We know that \(\cos(69^{\circ})\approx0.3584\). So \(x = 18\times0.3584=6.4512\approx6.5\)

Answer:

\(6.5\)