Question

Using the 60-30-90 right triangle method, find x and answer in simplest radical form.

Answer 1

Answer:

x = 2 $\sqrt{10}$

Step-by-step explanation:

Since the triangle is right we can use the sine ratio to find x

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{\sqrt{30} }{x}$

[ note the exact value of sin60° = $\frac{\sqrt{3} }{2}$ ], hence

$\frac{\sqrt{3} }{2}$ = $\frac{30}{x}$

multiply both sides by 2x, hence

$\sqrt{3}$ x = 2$\sqrt{30}$

divide both sides by $\sqrt{3}$

x = $\frac{2\sqrt{30} }{\sqrt{3} }$ = 2$\sqrt{\frac{30}{3} }$ = 2$\sqrt{10}$