Question

I need help solving this problem trigonometric function don't kind 22.)

Answer 1

Draw a diagram to visualize the situation:

Recall the definition of the sine of an angle:

`\sin \theta=\frac{\text{Side opposite to }\theta}{\text{ Hypotenuse}}`

In this case, the side opposite to θ has a measure of 80m, while the hypotenuse has a measure of 150m. Then:

`\begin{gathered} \sin \theta=(80m)/(150m) \\ \Rightarrow\sin \theta=(8)/(15) \end{gathered}`

Use the inverse sine function to isolate θ, and use a calculator to find its value:

`\Rightarrow\theta=\sin ^(-1)((8)/(15))=32.23095264\ldots`

Therefore, up to two decimal places:

`\theta=32.23^(\circ)`