Question

bentley leans a 22-foot ladder against a wall so that it forms an angle of 74° 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 the trigonometric relationship

We have a right triangle where the ladder is the hypotenuse (22 feet), the angle with the ground is \(74^\circ\), and the height up the wall is the opposite side to the angle. So we use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute values and solve

Let \(h\) be the height. Then \(\sin(74^\circ)=\frac{h}{22}\). Solving for \(h\), we get \(h = 22\times\sin(74^\circ)\). Calculate \(\sin(74^\circ)\approx0.9613\), so \(h\approx22\times0.9613 = 21.1486\).

Answer:

\(21.15\) (rounded to the nearest hundredth)