Question

a ladder leans against the side of a house. the angle of elevation of the ladder is 65°, and the top of the ladder is 13 ft above the ground. find the distance from the bottom of the ladder to the side of the house. round your answer to the nearest tenth.

Explanation:

Step1: Use the tangent function

In a right - triangle (formed by the house, the ground, and the ladder), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 65^{\circ}\), the opposite side \(y = 13\) ft, and the adjacent side is \(x\) (the distance we want to find). So, \(\tan65^{\circ}=\frac{13}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{13}{\tan65^{\circ}}\). Since \(\tan65^{\circ}\approx2.1445\), then \(x=\frac{13}{2.1445}\).

Step3: Calculate the value of \(x\)

\(x=\frac{13}{2.1445}\approx6.1\)

Answer:

\(6.1\)