Trigonometry Examples

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\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 4 \end{matrix} & \begin{matrix} A = & 90 \\ B = \\ C = & 40 \end{matrix} \end{matrix}

$\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 4 \end{matrix} & \begin{matrix} A = & 90 \\ B = \\ C = & 40 \end{matrix} \end{matrix}$

Step 1

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

\sin (C) = \frac{opp}{hyp}

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

Step 2

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

\sin (C) = \frac{c}{a}

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

Step 3

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

c

$c$ .

c = a \cdot \sin (C)

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

Step 4

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

c = a \cdot \sin (40)

$c = a \cdot \sin (40)$

Step 5

Multiply

4

$4$ by

0.6427876

$0.6427876$ .

c = 2.57115043

$c = 2.57115043$

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