Trigonometry Examples

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\begin{matrix} Side & Angle \begin{matrix} b = c = a = & 4 \end{matrix} & \begin{matrix} A = & 90 B = & 3 C = \end{matrix} \end{matrix}

$\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 4 \end{matrix} & \begin{matrix} A = & 90 \\ B = & 3 \\ C = \end{matrix} \end{matrix}$

Step 1

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos (B) = \frac{adj}{hyp}

$\cos (B) = \frac{adj}{hyp}$

Step 2

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

cos (B) = \frac{c}{a}

$\cos (B) = \frac{c}{a}$

Step 3

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

c

$c$ .

c = a \cdot cos (B)

$c = a \cdot \cos (B)$

Step 4

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

c = 4 \cdot cos (3)

$c = 4 \cdot \cos (3)$

Step 5

Multiply

4

$4$ by

0.99862953

$0.99862953$ .

c = 3.99451813

$c = 3.99451813$