Question

fatoumata leans a 30 - foot ladder against a wall so that it forms an angle of 62° with the ground. how high up the wall does the ladder reach? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 62^{\circ}\), the hypotenuse is \(30\) (length of the ladder), and the opposite side is \(x\) (height up the wall). So, \(\sin62^{\circ}=\frac{x}{30}\).

Step2: Solve for \(x\)

Multiply both sides by \(30\): \(x = 30\times\sin62^{\circ}\).
Using a calculator, \(\sin62^{\circ}\approx0.88295\). Then \(x = 30\times0.88295=26.4885\).

Answer:

\(26.5\)