Question

Two airplanes leave an airport, and the angle between their flight paths is 40°.
An hour later, one plane has traveled 300 miles while the other has traveled 200 miles.
How far apart are the airplanes at this time? Round your answer to the nearest mile.
A) 195 miles
B) 250 miles
C) 360 miles
D) 423 miles

Answer 1

I think the answer is d

Answer 2

In the right angle triangle the ratio of the hypotenuse to the opposite side is equal to the sin angle. Both the planes are 99 miles away from each other after one hour.

Angles of right angle triangle

In the right angle triangle the ratio of the hypotenuse to the opposite side is equal to the sin angle.

Let suppose height of the plane first plane who traveled 300 miles is x meter. Then,

$\sin 40=\dfrac{x}{300}$

Solve for the x,

$x=\sin(40) \times 300\\ x=192.83$

Let suppose height of the second plane who traveled 200 miles is y meter. Then,

$\sin 40=\dfrac{y}{200}$

Solve for the y,

$x=\sin(40) \times 200\\ x=128.55$

The difference of height between both the planes is,

$d=192.33-128.55\\ d=63.78$

The distance between their height is 63.78 and the angle is still 40 degrees. Let the distance between both the plans after one hour is l miles. Thus,

$\sin 40=\dfrac{63.78}{l}$

Solve for l, we get,

$l=98.74$

Thus both the planes are 99 miles away from each other after one hour.

Learn more about the right angle triangle here;

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