Question

maria is flying a helicopter at 1,350 feet and sees an airplane 2,400 horizontal feet in front of her, but is also unknown vertical distance above her. maria knows the angle of elevation is 54 degrees. how far is the airplane from the ground? (1 point)
4,654 feet
3,003 feet
4,653 feet
4,600 feet

Explanation:

Step1: Set up tangent - ratio equation

Let the vertical distance of the airplane above Maria be $y$. We know that $\tan\theta=\frac{y}{x}$, where $\theta = 54^{\circ}$ and $x = 2400$ feet. So, $\tan(54^{\circ})=\frac{y}{2400}$.

Step2: Solve for $y$

Since $\tan(54^{\circ})\approx1.37638$, then $y = 2400\times\tan(54^{\circ})\approx2400\times1.37638 = 3303.312$ feet.

Step3: Find the height of the airplane from the ground

The helicopter is at 1350 feet. The height of the airplane from the ground $h=y + 1350$. So, $h=3303.312+1350=4653.312\approx4653$ feet.

Answer:

4653 feet