ANSWER
[tex]y = 7 \sqrt{2} [/tex]
[tex]x = 7[/tex]
EXPLANATION
The given triangle has a right angle.
The side opposite to the 45° angle is 7 units.
To find angle x, we use the tangent ratio.
Recall the mnemonics TOA, which means,
[tex] \tan(45 \degree) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(45 \degree) = \frac{7}{x} [/tex]
[tex]1 = \frac{7}{x} [/tex]
[tex]x = 7[/tex]
To find y, we use the sine ratio, which means
[tex] \sin(45 \degree) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin(45 \degree) = \frac{7}{y} [/tex]
[tex]y= \frac{7}{\sin(45 \degree) } [/tex]
[tex]y= \frac{7}{ \frac{1}{ \sqrt{2} } } [/tex]
[tex]y = 7 \times \frac{ \sqrt{2} }{1} [/tex]
[tex]y = 7 \sqrt{2} [/tex]
