Question

1. a wooden beam 24 feet long leans against a wall and makes and angle of 71° with the ground. how high up the wall does the beam reach?

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the length of the beam is the hypotenuse ($c = 24$ feet) and we want to find the height $h$ (opposite side) with respect to the given angle $\theta=71^{\circ}$. We use the sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin\theta=\frac{h}{c}$

Step2: Solve for $h$

Substitute $\theta = 71^{\circ}$ and $c = 24$ into the formula.
$h = c\times\sin\theta$
$h=24\times\sin(71^{\circ})$
We know that $\sin(71^{\circ})\approx0.9455$.
$h = 24\times0.9455=22.692$ feet.

Answer:

Approximately 22.7 feet