Trigonometry Examples

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 2 \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$

Step 1

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

$\tan (B) = \frac{opp}{adj}$

Step 2

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

$\tan (B) = \frac{b}{a}$

Step 3

Set up the equation to solve for the opposite side, in this case $b$ .

$b = a \cdot \tan (B)$

Step 4

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

$b = 2 \cdot \tan (60)$

Step 5

Multiply $2$ by $\sqrt{3}$ .

$b = 2 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = 2 \sqrt{3}$

Decimal Form:

$b = 3.46410161 \dots$