Find the missing lengths of the sides

ANSWER
The correct answer is C
EXPLANATION
The given triangle is a right triangle. Since two angles are equal, it is a right isosceles triangle.
This implies that, x=8 units.
Using Pythagoras Theorem,
[tex] {y}^{2} = {8}^{2} + {8}^{2} [/tex]
This implies that:
[tex]{y}^{2} = 64 + 64[/tex]
[tex]{y}^{2} =128[/tex]
Take positive square root,
[tex]{y} = \sqrt{128} [/tex]
[tex]{y} = 8 \sqrt{2} [/tex]
The correct answer is C
Answer:
Correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].
Step-by-step explanation:
Apply formula [tex]\sin\left(\theta\right)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sin\left(45^o\right)=\frac{8}{y}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{8}{y}[/tex]
[tex]y=8\sqrt{2}[/tex]
Apply formula [tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]
[tex]\tan\left(45^o\right)=\frac{8}{x}[/tex]
[tex]1=\frac{8}{x}[/tex]
[tex]x=8[/tex]
Hence correct choice is C. [tex]x=8[/tex], [tex]y=8\sqrt{2}[/tex].