Trigonometry Examples

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 5 \\ a = \end{matrix} & \begin{matrix} A = & 45 \\ B = & 45 \\ C = & 90 \end{matrix} \end{matrix}$

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.

$a = c \cdot \sin (45)$

Step 5

Combine $5$ and $\frac{\sqrt{2}}{2}$ .

$a = \frac{5 \sqrt{2}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{5 \sqrt{2}}{2}$

Decimal Form:

$a = 3.53553390 \dots$