Question

Find the missing side lengths. Leave your answer as radicals in simplest form.

Answer 1

Answer:

x = y = 2

Step-by-step explanation:

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

sin45° = $\frac{1}{\sqrt{2} }$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{2\sqrt{2} }$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

x $\sqrt{2}$ = 2$\sqrt{2}$ ( divide both sides by $\sqrt{2}$ )

x = 2

The triangle is isosceles, base angles both 45°, then legs are congruent, so

x = y = 2