Trigonometry Examples

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 21 \\ c = & 29 \\ a = & 20 \end{matrix} & \begin{matrix} A = \\ B = \\ C = & 90 \end{matrix} \end{matrix}$

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 $29$ of the triangle.

$B = \arcsin (\frac{21}{29})$

Step 1.3

Evaluate $\arcsin (\frac{21}{29})$ .

$B = 46.39718102$

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.

$A + 90 + 46.39718102 = 180$

Step 2.2

Solve the equation for $A$ .

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Step 2.2.1

Add $90$ and $46.39718102$ .

$A + 136.39718102 = 180$

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 $136.39718102$ from both sides of the equation.

$A = 180 - 136.39718102$

Step 2.2.2.2

Subtract $136.39718102$ from $180$ .

$A = 43.60281897$

Step 3

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

$A = 43.60281897$

$B = 46.39718102$

$C = 90$

$a = 20$

$b = 21$

$c = 29$