Trigonometry Examples

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 12 \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$

Step 1

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

$\sin (A) = \frac{opp}{hyp}$

Step 2

Substitute the name of each side into the definition of the sine function.

$\sin (A) = \frac{a}{c}$

Step 3

Set up the equation to solve for the hypotenuse, in this case $c$ .

$c = \frac{a}{\sin (A)}$

Step 4

Substitute the values of each variable into the formula for sine.

$c = \frac{12}{\sin (30)}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$c = 12 \cdot 2$

Step 6

Multiply $12$ by $2$ .

$c = 24$