Question

Find the value of each variable

Answer 1

$x = 15 \sqrt{2}$

$y = 15 \sqrt{2}$

Answer 2

Answer:

x = y = 15$\sqrt{2}$

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = $\frac{\sqrt{2} }{2}$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{30}$ ( multiply both sides by 30 )

30 × sin45° = x , then

x = 30 × $\frac{\sqrt{2} }{2}$ = 15$\sqrt{2}$

The triangle is a right isosceles triangle thus the legs are congruent, then

x = y = 15$\sqrt{2}$