Find the value of the variable. If your answer is not an integer, leave it in simplest radical form. 5√(2) (5√(2) )/(2) 5√(3) (5√(3))/(2)

Question

Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.


`5√(2)`

`(5√(2) )/(2)`

`5√(3)`

`(5√(3))/(2)`

Answer 1

`$(5√(2) )/(2)$`

Explanation:

`x: \text{opposite side of the angle of 45\º}`

`5: \text{hypotenuse of the right triangle}`

`$\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=(x)/(5) $`

`$\text{Once }\sin(45\º)=(√(2) )/(2) $`

`$(√(2) )/(2) =(x)/(5) \Rightarrow 2x=5√(2) \Rightarrow x=(5√(2) )/(2) $`

You can just remember that 5 is the diagonal of a square of side length x.

`$5=x√(2) \Rightarrow x=(5)/(√(2) ) \Rightarrow x=(5)/(√(2) ) \cdot (√(2) )/(√(2) ) = (5√(2) )/(2) $`