Question

3. Find the missing side lengths. Leave the answers as radicals in simplest form.

Answer 1

Answer:

x = y = 6.5$\sqrt{2}$

Step-by-step explanation:

the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y

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

sin45° = $\frac{\sqrt{2} }{2}$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{13}$ = $\frac{\sqrt{2} }{2}$ ( cross- multiply )

2x = 13$\sqrt{2}$ ( divide both sides by 2 )

x = y = 6.5$\sqrt{2}$