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 round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trig - function

We have a right - triangle situation where the ladder is the hypotenuse ($c = 120$ feet) and we want to find the height (opposite side to the given angle $\theta=79^{\circ}$). We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin\theta=\frac{h}{c}$

Step2: Substitute the values

Substitute $\theta = 79^{\circ}$ and $c = 120$ into the sine formula. $\sin(79^{\circ})=\frac{h}{120}$.
We know that $\sin(79^{\circ})\approx0.9816$. So, $0.9816=\frac{h}{120}$.

Step3: Solve for $h$

Multiply both sides of the equation by 120: $h = 120\times\sin(79^{\circ})$.
$h=120\times0.9816 = 117.792$.

Answer:

$117.79$ feet