Trigonometry Examples

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\begin{matrix} Side & Angle \begin{matrix} b = c = a = & 2 \end{matrix} & \begin{matrix} A = & 90 B = & 1 C = \end{matrix} \end{matrix}

$\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = \\ a = & 2 \end{matrix} & \begin{matrix} A = & 90 \\ B = & 1 \\ C = \end{matrix} \end{matrix}$

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 = 2 \cdot cos (1)

$c = 2 \cdot \cos (1)$

Step 5

Multiply

2

$2$ by

0.99984769

$0.99984769$ .

c = 1.99969539

$c = 1.99969539$