Trigonometry Examples

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 10 \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$

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 opposite side, in this case $a$ .

$a = c \cdot \sin (A)$

Step 4

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

$a = c \cdot \sin (30)$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $10$ .

$a = 2 (5) \cdot \frac{1}{2}$

Step 5.2

Cancel the common factor.

$a = 2 \cdot 5 \cdot \frac{1}{2}$

Step 5.3

Rewrite the expression.

$a = 5$