High School

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An airplane rises at an angle of [tex]15^\circ[/tex] with the ground. Find, to the nearest 10 feet, the distance it has flown when it has covered a horizontal distance of 1500 feet.

Answer :

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.

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