Question

Solve for the indicated side. Leave your answer in simplified radical form. (Step by step)

Answer 1

In order to solve this particular question, use the sine rule.

$\sf sin(x)= \dfrac{opposite}{hypotensue}$

Here given:

• opposite = 6 inch

• hypotenuse = x

• angle = 60°

Henceforth solve:

$\hookrightarrow \sf sin(60)= \dfrac{6}{x}$

$\hookrightarrow \sf x= \dfrac{6}{sin(60)}$

$\hookrightarrow \sf x= 4\sqrt{3}$

Answer 2

$\\ \rm\rightarrowtail sin60=\dfrac{Perpendicular}{Hypotenuse}$

$\\ \rm\rightarrowtail sin60=\dfrac{6}{x}$

$\\ \rm\rightarrowtail \dfrac{\sqrt{3}}{2}=\dfrac{6}{x}$

$\\ \rm\rightarrowtail \sqrt{3}x=12$

$\\ \rm\rightarrowtail x=12/\sqrt{3}$

$\\ \rm\rightarrowtail x=4\sqrt{3}in$