Question

Special triangles 45-45-90​

Answer 1

9514 1404 393

Answer:

  x = y = (√10)/2

Step-by-step explanation:

In an isosceles right triangle, the side lengths are equal, and they are equal to (√2)/2 times the hypotenuse length.

  x = y = (√5)(√2)/2

  x = y = (√10)/2

Answer 2

Answer:

x = y = $\frac{1}{2}$ $\sqrt{10}$

Step-by-step explanation:

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

sin45° = $\frac{\sqrt{2} }{2}$

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{\sqrt{5} }$ = $\frac{\sqrt{2} }{2}$ ( cross- multiply )

2x = $\sqrt{10}$ ( divide both sides by 2 )

x = $\frac{1}{2}$ $\sqrt{10}$

Since the base angles are 45° then the triangle is isosceles with both legs congruent , thus

x = y = $\frac{1}{2}$ $\sqrt{10}$