Use √(x) Solve for x

Question

Use
`√(x)` Solve for x

Answer 1

Check the picture below.

and if you check your Unit Circle, you'd notice that those angles have an specific value.

`\cfrac{15}{sin(60^o)}~~ = ~~\cfrac{x}{sin(45^o)}\implies \cfrac{15}{~~ (√(3))/(2)~~}~~ = ~~\cfrac{x}{~~ (√(2))/(2)~~}\implies \cfrac{15}{1}\cdot \cfrac{2}{√(3)}~~ = ~~\cfrac{x}{1}\cdot \cfrac{2}{√(2)}`

`\cfrac{30}{√(3)}=\cfrac{2x}{√(2)}\implies \cfrac{30√(2)}{√(3)}=2x\implies \cfrac{30√(2)}{2√(3)}=x\implies \cfrac{15√(2)}{√(3)}=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{rationalizing the denominator}}{\cfrac{15√(2)}{√(3)}\cdot \cfrac{√(3)}{√(3)}\implies \cfrac{15√(6)}{3}}\implies \boxed{5√(6)=x}`