Question

Find the value of each variable

Answer 1

x = y = 15
`√(2)`

Explanation:

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

sin45° =
`(√(2) )/(2)` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(x)/(30)` ( multiply both sides by 30 )

30 × sin45° = x , then

x = 30 ×
`(√(2) )/(2)` = 15
`√(2)`

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

x = y = 15
`√(2)`

Answer 2

`x = 15 √(2)`

`y = 15 √(2)`