Question

andres leans a 22 - foot ladder against a wall so that it forms an angle of 73° 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 the sine function

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 73^{\circ}$, the hypotenuse is the length of the ladder ($22$ feet), and the opposite side is the height on the wall ($x$). So, $\sin(73^{\circ})=\frac{x}{22}$.

Step2: Solve for $x$

Multiply both sides of the equation by $22$: $x = 22\times\sin(73^{\circ})$.
We know that $\sin(73^{\circ})\approx0.9563$. Then $x = 22\times0.9563$.
$x=22\times0.9563 = 21.0386$.

Answer:

$21.0$ feet