Draw a diagram to visualize the situation:
Recall the definition of the sine of an angle:
[tex]\sin \theta=\frac{\text{Side opposite to }\theta}{\text{ Hypotenuse}}[/tex]
In this case, the side opposite to θ has a measure of 80m, while the hypotenuse has a measure of 150m. Then:
[tex]\begin{gathered} \sin \theta=\frac{80m}{150m} \\ \Rightarrow\sin \theta=\frac{8}{15} \end{gathered}[/tex]
Use the inverse sine function to isolate θ, and use a calculator to find its value:
[tex]\Rightarrow\theta=\sin ^{-1}(\frac{8}{15})=32.23095264\ldots[/tex]
Therefore, up to two decimal places:
[tex]\theta=32.23^{\circ}[/tex]
