To find the height of the airplane above the ground, we can use trigonometry. We have a right triangle where:
- The height Marna is flying at is \( 1,350 \) feet (this is the height of Marna's helicopter).
- The horizontal distance between Marna and the airplane is \( 2,400 \) feet.
- The angle of elevation from Marna's helicopter to the airplane is \( 54^{\circ} \).
Let \( h \) be the height of the airplane above the ground. The vertical distance from Marna to the airplane is then \( h - 1,350 \) feet.
Using the tangent function, we can relate the angle of elevation to the opposite and adjacent sides of the triangle:
\[ \tan(54^{\circ}) = \frac{h - 1,350}{2,400} \]
Now, we can solve for \( h \):
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Calculate \( \tan(54^{\circ}) \): \[ \tan(54^{\circ}) \approx 1.3764 \]
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Substitute this value into the equation: \[ 1.3764 = \frac{h - 1,350}{2,400} \]
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Multiply both sides by \( 2,400 \): \[ 1.3764 \times 2,400 = h - 1,350 \] \[ 3,302.56 = h - 1,350 \]
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Solve for \( h \): \[ h = 3,302.56 + 1,350 \] \[ h \approx 4,652.56 \text{ feet} \]
Therefore, rounding to the nearest whole number, the height of the airplane above the ground is approximately \( 4,653 \) feet.
Thus, the answer is 4,653 feet.