Answer:
The distance flown by the airplane to nearest tenth of a feet = 1550 ft.
Step-by-step explanation:
Given:
Then angle at which the airplane rises = 15°
Horizontal distance it has covered = 1500 ft
To find the distance it has flown to nearest tenth feet.
Solution:
On tracing the path of the plane, we can draw a right triangle such that the adjacent side is 1500 feet and the angle of elevation is 15°.
We need the hypotenuse of the right triangle as it represents the distance flown by the airplane..
Applying trigonometric ratio:
[tex]\cos\theta = \frac{Adjacent\ side}{Hypotenuse}[/tex]
Let hypotenuse be = [tex]x[/tex]
Plugging in the given values.
[tex]\cos 15\°=\frac{1500}{x}[/tex]
Multiplying both sides by [tex]x[/tex]
[tex]x\cos15\°=\frac{1500}{x}.x[/tex]
[tex]x\cos15\°=1500[/tex]
Dividing both sides by [tex]cos15\°[/tex].
[tex]\frac{x\cos15\°}{\cos 15\°}=\frac{1500}{\cos 15\°}[/tex]
∴ [tex]x=1552.91[/tex]
Thus, the distance flown by the airplane to nearest tenth of a feet = 1550 ft.
