Trigonometry Examples

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 12 \\ c = & 37 \\ a = & 35 \end{matrix} & \begin{matrix} A = \\ B = \\ C = & 90 \end{matrix} \end{matrix}$

Step 1

Find $B$ .

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Step 1.1

The angle $B$ can be found using the inverse sine function.

$B = \arcsin (\frac{opp}{hyp})$

Step 1.2

Substitute in the values of the opposite side to angle $B$ and hypotenuse $37$ of the triangle.

$B = \arcsin (\frac{12}{37})$

Step 1.3

Evaluate $\arcsin (\frac{12}{37})$ .

$B = 18.92464441$

Step 2

Find the last angle of the triangle.

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Step 2.1

The sum of all the angles in a triangle is $180$ degrees.

$A + 90 + 18.92464441 = 180$

Step 2.2

Solve the equation for $A$ .

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Step 2.2.1

Add $90$ and $18.92464441$ .

$A + 108.92464441 = 180$

Step 2.2.2

Move all terms not containing $A$ to the right side of the equation.

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Step 2.2.2.1

Subtract $108.92464441$ from both sides of the equation.

$A = 180 - 108.92464441$

Step 2.2.2.2

Subtract $108.92464441$ from $180$ .

$A = 71.07535558$

Step 3

These are the results for all angles and sides for the given triangle.

$A = 71.07535558$

$B = 18.92464441$

$C = 90$

$a = 35$

$b = 12$

$c = 37$