Question

Marna is flying a helicopter at 1,350 feet and sees an airplane 2,400 horizontal feet in front of her, but is also an unknown vertical distance above her. Marna knows the angle of elevation is 54 degrees. How far is the airplane from the ground?(1 point) Responses 5,245 feet 5,245 feet 4,714 feet 4,714 feet 3,303 feet 3,303 feet 4,653 feet

Answer 1

To find the height of the airplane above the ground, we can use trigonometry. We know the following:

- Marna's altitude (height) is 1,350 feet.
- The horizontal distance (adjacent side) to the airplane is 2,400 feet.
- The angle of elevation to the airplane is 54 degrees.

Using the tangent function, we can first find the vertical distance (h) from Marna to the airplane:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Here, \(\theta = 54\) degrees, the opposite side is the vertical distance \(h\), and the adjacent side is 2,400 feet. Thus, we can set up the equation:

\[
\tan(54^\circ) = \frac{h}{2400}
\]

To find \(h\):

\[
h = 2400 \times \tan(54^\circ)
\]

Calculating \(\tan(54^\circ)\):

\[
\tan(54^\circ) \approx 1.37638
\]

Now, substituting this value:
\[
h \approx 2400 \times 1.37638 \approx 3304.63 \text{ feet}
\]

Now, adding this vertical distance \(h\) to Marna's height of 1,350 feet to find the height of the airplane above ground:

\[
\text{Height of airplane} = 1350 + h \approx 1350 + 3304.63 \approx 4654.63 \text{ feet}
\]

Rounding, we can see that the height of the airplane is approximately 4,655 feet.

Among the options provided, the closest answer is **4,653 feet**.