Question

parker leans a 16 - foot ladder against a wall so that it forms an angle of 64° with the ground. how high up the wall does the ladder reach? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 64^{\circ}\), the hypotenuse is \(16\) (length of the ladder), and the opposite side is \(x\) (height up the wall). So, \(\sin(64^{\circ})=\frac{x}{16}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(64^{\circ})=\frac{x}{16}\) by \(16\). We get \(x = 16\times\sin(64^{\circ})\).
Using a calculator, \(\sin(64^{\circ})\approx0.8988\). Then \(x=16\times0.8988 = 14.3808\approx14.38\).

Answer:

\(14.38\)