Question

Find the length of the sides of the special triangles that are labeled with variables. If necessary round any answers to one decimal place.

Answer 1

`y=12.7\text{ in}`

Explanation:

To find the length of y, we can use trigonometric ratios, which are described by the following equations:

`\begin{gathered} \sin (\text{angle)=}\frac{opposite}{\text{hypotenuse}}_{} \\ \cos (\text{angle)}=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{tan(angle)}=\frac{\text{ opposite}}{\text{ adjacent}} \end{gathered}`

Therefore, to find y, use the sin relationship:

`\begin{gathered} \sin (45)=(9)/(y) \\ y=(9)/(\sin (45)) \\ y=12.7\text{ in} \end{gathered}`