x=11.3 y=8
Explanationhere we have a right triangle, so we can use a trigonometric function to find the missing sides
so
Step 1
a)let
[tex]\begin{gathered} angle=45\text{ \degree} \\ opposite\text{ side=8} \\ adjacent\text{ side=y} \\ hypotenuse=x \end{gathered}[/tex]
Step 2
now, fin the missing length
a) y
to find the adjacent side we can use the stan function
[tex]tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]
replace and solve for y( adjacent side)
[tex]\begin{gathered} tan45=\frac{8}{y} \\ y=\frac{8}{tan\text{ 45}}=\frac{8}{1} \\ y=8 \end{gathered}[/tex]
b)x (hypotenuse)
to find the hyoptenuse we can use the sin function ,
[tex]\sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]
replace and solve for x
[tex]\begin{gathered} sin\text{ 45=}\frac{8}{x} \\ x=\frac{8}{sin\text{ 45}}=11.3 \\ x=11.3 \end{gathered}[/tex]
therefore, the answer is
x=11.3 y=8
I hope this helps you
