To find the height of the airplane from the ground, we can use the tangent function, which relates the angle of elevation, the vertical distance, and the horizontal distance.
Let \( h \) be the vertical distance above Marna's helicopter to the airplane. Marna is at a height of 1,350 feet above the ground. The horizontal distance to the airplane is 2,400 feet, and the angle of elevation to the airplane is 54 degrees.
The formula for the tangent of the angle can be expressed as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, the opposite side is the vertical distance \( h \), and the adjacent side is 2,400 feet. Thus, we can express this as:
\[ \tan(54^\circ) = \frac{h}{2400} \]
First, we can calculate \( \tan(54^\circ) \):
\[ \tan(54^\circ) \approx 1.3764 \]
Setting up the equation, we can solve for \( h \):
\[ 1.3764 = \frac{h}{2400} \]
Thus,
\[ h = 1.3764 \times 2400 \approx 3303.36 \text{ feet} \]
Now, to find the total height of the airplane above the ground, we add the height of Marna's helicopter:
\[ \text{Height of the airplane from the ground} = 1350 + 3303.36 \approx 4653.36 \text{ feet} \]
Therefore, rounding to the nearest whole number, the airplane is approximately 4,653 feet above the ground.
The correct answer is:
4,653 feet.
1 answer