Question

nabhitha leans a 26 - foot ladder against a wall so that it forms an angle of 61° 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, \(\theta = 61^{\circ}\), the hypotenuse \(c = 26\) and the adjacent side is \(x\). So, \(\cos(61^{\circ})=\frac{x}{26}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(61^{\circ})=\frac{x}{26}\) by \(26\). We get \(x = 26\times\cos(61^{\circ})\).
Since \(\cos(61^{\circ})\approx0.4848\), then \(x=26\times0.4848\).
\(x = 12.6048\)

Answer:

\(12.60\) feet