Question

A rocket is fired from the ground at some angle and travels in a straight path. When the rocket has traveled 460 yards it is 300 yards above the ground. At what angle (in radians) was the rocket fired at?θ=

Answer 1

A rocket is fired from the ground at some angle and travels in a straight path.

When the rocket has traveled 460 yards it is 300 yards above the ground.

At what angle (in radians) was the rocket fired at?

Let us draw a diagram to better understand the problem.

Recall from the trigonometric ratios,

`\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}`

Let us solve for the angle θ in radians

`\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=(300)/(460) \\ \theta=\sin ^(-1)((300)/(460)) \\ \theta=0.71\: \text{radians} \end{gathered}`

Therefore, the rocket was fired at an angle of 0.71 radians.