Question

A plane took off at a 15° angle to the ground and flew in this direction. She is standing at a .25 miles from the point where the plane took off. If the plane is traveling 20 miles in the air, about how far is Sydney from the airplane? Round your answer to the nearest whole number.

Answer 1

To find the distance from Sydney to the airplane, use trigonometry. The distance is approximately 0.067 miles, rounded to the nearest whole number.

Step-by-step explanation:

To find the distance from Sydney to the airplane, we can use trigonometry. Since the angle of elevation of the plane is given as 15°, we can use the tangent function to calculate the distance.

Tangent(angle) = Opposite/Adjacent

In this case, the adjacent side is the distance between the student and the point where the plane took off, which is given as 0.25 miles. The opposite side is the distance we want to find, and the angle is 15°.

So, we can rearrange the equation to find the opposite side:

Opposite = Tangent(angle) * Adjacent

Opposite = Tan(15°) * 0.25 miles

Using a calculator, we find that Tan(15°) ≈ 0.268, so the distance from Sydney to the airplane is approximately 0.268 * 0.25 miles ≈ 0.067 miles. Rounding to the nearest whole number, Sydney is about 0 miles from the airplane.