Question

ving for side lengths of right triangles a 15-foot ladder is leaning against a wall. the ladder makes a 51° angle with the ground. how high on the wall does the ladder reach? round to the nearest tenth. enter your answer in the box. feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the ladder is the hypotenuse (\(c = 15\) feet), the angle with the ground is \(\theta=51^\circ\), and we need to find the height on the wall (\(a\)), which is the opposite side to the angle \(\theta\). The sine function relates the opposite side and the hypotenuse: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(51^\circ)=\frac{a}{15}\).

Step2: Solve for \(a\)

Rearrange the formula to solve for \(a\): \(a = 15\times\sin(51^\circ)\). Calculate \(\sin(51^\circ)\approx0.7771\). Then \(a = 15\times0.7771\approx11.6565\). Round to the nearest tenth.

Answer:

11.7