Question

question 2
1 pts
1200 ft.
48°
flight 4358 took off from the dfw airport at an elevation of 48°. if the airplane has been traveling for 1200 ft., approximately how far above the ground is the airplane?
1614
802
1793
891

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the hypotenuse is 1200 ft (the distance the airplane has traveled) and we need to find the opposite side (height above ground, \( x \)) to the angle of elevation \( 48^\circ \). The sine function relates the opposite side and the hypotenuse: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).

Step2: Set up the equation

Using the sine formula: \( \sin(48^\circ) = \frac{x}{1200} \).

Step3: Solve for \( x \)

Multiply both sides by 1200: \( x = 1200 \times \sin(48^\circ) \). Calculate \( \sin(48^\circ) \approx 0.7431 \), so \( x \approx 1200 \times 0.7431 \approx 891.72 \), which is approximately 891.

Answer:

891 (corresponding to the option: 891)