Question

Special triangles 45-45-90​

Answer 1

x = y =
`(1)/(2)`
`√(10)`

Explanation:

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

sin45° =
`(√(2) )/(2)`

sin45° =
`(opposite)/(hypotenuse)` =
`(x)/(√(5) )` =
`(√(2) )/(2)` ( cross- multiply )

2x =
`√(10)` ( divide both sides by 2 )

x =
`(1)/(2)`
`√(10)`

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

x = y =
`(1)/(2)`
`√(10)`

Answer 2

9514 1404 393

Answer:

x = y = (√10)/2

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