Question

rashaad leans a 22 - foot ladder against a wall so that it forms an angle of 65° 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 ($c = 22$ feet), the height up the wall is the side opposite the given angle ($\theta=65^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute the values into the formula

Let $h$ be the height up the wall. Then $\sin(65^{\circ})=\frac{h}{22}$.

Step3: Solve for $h$

Multiply both sides by 22: $h = 22\times\sin(65^{\circ})$.
We know that $\sin(65^{\circ})\approx0.9063$.
So $h=22\times0.9063 = 19.9386$.

Answer:

$19.94$ feet