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: Identify trigonometric ratio

The ladder is hypotenuse (16ft), height \(x\) is opposite \(64^\circ\). Use \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Set up equation

\(\sin(64^\circ)=\frac{x}{16}\) → \(x=16\times\sin(64^\circ)\).

Step3: Calculate value

Compute \(\sin(64^\circ)\approx0.8988\), so \(x\approx16\times0.8988=14.3808\).

Step4: Round to nearest hundredth

14.3808 ≈ 14.38.

Answer:

14.38