Question

Find the length of side

x in simplest radical form with a rational denominator.



Thanks in advance

Answer 1

x = 2

Explanation:

sin(45)/x = sin(90)/
`√(8)`

`\sin \left(45^(\circ \:)\right)=(√(2))/(2)`

x =
`√(8)`
`\sin \left(45^(\circ \:)\right)`

`x = √(8) (√(2))/(2)`

x =
`(√(16) )/(2)`

x = 4/2

x = 2

Answer 2

2

Explanation:

Pythagoras. c² = a² + b²

since both "side angles" are equal (45 degrees), we know it is an isosceles triangle, that means also the other side = x.

and so,

8 = x² + x² = 2x²

4 = x²

x = 2