Trigonometry Examples

$A = 30$ , $a = 6.59$ , $b = 13.18$ , $B = 90$

Step 1

Find the last angle of the triangle.

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Step 1.1

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

$30 + C + 90 = 180$

Step 1.2

Solve the equation for $C$ .

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Step 1.2.1

Add $30$ and $90$ .

$C + 120 = 180$

Step 1.2.2

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

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Step 1.2.2.1

Subtract $120$ from both sides of the equation.

$C = 180 - 120$

Step 1.2.2.2

Subtract $120$ from $180$ .

$C = 60$

Step 2

Find the last side of the triangle using the Pythagorean theorem.

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Step 2.1

Use the Pythagorean theorem to find the unknown side. In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (the two sides other than the hypotenuse).

$a^{2} + b^{2} = c^{2}$

Step 2.2

Solve the equation for $c$ .

$c = \sqrt{b^{2} - a^{2}}$

Step 2.3

Substitute the actual values into the equation.

$c = \sqrt{{(13.18)}^{2} - {(6.59)}^{2}}$

Step 2.4

Raise $13.18$ to the power of $2$ .

$c = \sqrt{173.7124 - {(6.59)}^{2}}$

Step 2.5

Raise $6.59$ to the power of $2$ .

$c = \sqrt{173.7124 - 1 \cdot 43.4281}$

Step 2.6

Multiply $- 1$ by $43.4281$ .

$c = \sqrt{173.7124 - 43.4281}$

Step 2.7

Subtract $43.4281$ from $173.7124$ .

$c = \sqrt{130.2843}$

Step 3

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

$A = 30$

$B = 90$

$C = 60$

$a = 6.59$

$b = 13.18$

$c = \sqrt{130.2843}$