Question

a rocket is fired from the ground at some angle and travels in a straight path. when the rocket has traveled 440 yards it is 320 yards above the ground. at what angle (in degrees) was the rocket fired?

Answer 1

Using trigonometry and converting the given distances from yards to meters, the angle at which the rocket was fired is calculated using the arctan function to be approximately 36.04 degrees above the horizontal.

Step-by-step explanation:

To determine the angle at which the rocket was fired, we need to use trigonometry. Given that the rocket has traveled 440 yards in distance and is 320 yards above the ground, we can use the tangent function which relates the angle of a right triangle to the ratio of the opposite side over the adjacent side.

First, we convert the distances from yards to meters because the standard unit for these types of calculations is meters (1 yard = 0.9144 meters). Therefore, the horizontal distance (adjacent) is 440 yards * 0.9144 m/yard = 402.336 meters and the vertical distance (opposite) is 320 yards * 0.9144 m/yard = 292.608 meters.

Now, the tangent of the angle θ is equal to the opposite side divided by the adjacent side:

θ = arctan(opposite/adjacent)

θ = arctan(292.608 / 402.336)

θ = arctan(0.727)

θ ≈ 36.04°

The rocket was fired at an angle of approximately 36.04 degrees above the horizontal.