Question

a fire truck extends a 120 foot ladder toward a building at a 79° angle, to reach a window. how high is the window above the fire truck? feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 120$ feet) and the height of the window above the fire - truck is the side opposite the given angle ($\theta=79^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
So, $\sin(79^{\circ})=\frac{h}{120}$, where $h$ is the height.

Step2: Solve for $h$

Rearrange the formula to get $h = 120\times\sin(79^{\circ})$.
We know that $\sin(79^{\circ})\approx0.9816$.
Then $h = 120\times0.9816$.
$h=117.792$.

Answer:

$117.79$ feet