Question

Kabir is flying a helicopter at an elevation of 1,350 feet. He sees an airplane 2,400 horizontal feet in front of him, but doesn't know how far the plane is above him. If the angle of elevation is 54 degrees, how far is the airplane from the ground?



(1 point)
Responses

3,303 feet
3,303 feet

5,245 feet
5,245 feet

4,653 feet
4,653 feet

4,414 feet
4,414 feet
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Answer 1

To find the altitude of the airplane, we can use the information provided about the angle of elevation and the horizontal distance.

1. **Identify the known values:**
- Kabir's elevation = 1,350 feet
- Horizontal distance to the airplane = 2,400 feet
- Angle of elevation = 54 degrees

2. **Use the tangent of the angle:**
The tangent of the angle of elevation is defined as the opposite side (the difference in height between the helicopter and the airplane) over the adjacent side (the horizontal distance to the airplane).

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

Here, we can denote the height of the airplane above the ground as \( h \). The difference in height between the airplane and the helicopter is \( h - 1350 \).

\[
\tan(54^\circ) = \frac{h - 1350}{2400}
\]

3. **Calculate \( \tan(54^\circ) \):**
\[
\tan(54^\circ) \approx 1.3764
\]

4. **Substituting the values into the equation:**
\[
1.3764 = \frac{h - 1350}{2400}
\]

5. **Solve for \( h \):**
\[
h - 1350 = 1.3764 \times 2400
\]
\[
h - 1350 = 3303.36
\]
\[
h = 3303.36 + 1350
\]
\[
h \approx 4653.36 \text{ feet}
\]

6. **Round to the nearest whole number:**
The altitude of the airplane is approximately 4,653 feet.

Thus, the answer is:

**4,653 feet**