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,
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]Let us solve for the angle θ in radians
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=\frac{300}{460} \\ \theta=\sin ^{-1}(\frac{300}{460}) \\ \theta=0.71\: \text{radians} \end{gathered}[/tex]Therefore, the rocket was fired at an angle of 0.71 radians.
