Trigonometry Examples

$A = 8$ ,

$a = 30$ ,

$c = 145$ ,

$B = 90$

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.

$8 + C + 90 = 180$

Step 1.2

Solve the equation for

$C$ .

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Step 1.2.1

Add

$8$ and

$90$ .

$C + 98 = 180$

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

$98$ from both sides of the equation.

$C = 180 - 98$

Step 1.2.2.2

Subtract

$98$ from

$180$ .

$C = 82$

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

$b$ .

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

Step 2.3

Substitute the actual values into the equation.

$b = \sqrt{{(145)}^{2} + {(30)}^{2}}$

Step 2.4

Raise

$145$ to the power of

$2$ .

$b = \sqrt{21025 + {(30)}^{2}}$

Step 2.5

Raise

$30$ to the power of

$2$ .

$b = \sqrt{21025 + 900}$

Step 2.6

Add

$21025$ and

$900$ .

$b = \sqrt{21925}$

Step 2.7

Rewrite

$21925$ as

$5^{2} \cdot 877$ .

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Step 2.7.1

Factor

$25$ out of

$21925$ .

$b = \sqrt{25 (877)}$

Step 2.7.2

Rewrite

$25$ as

$5^{2}$ .

$b = \sqrt{5^{2} \cdot 877}$

Step 2.8

Pull terms out from under the radical.

$b = 5 \sqrt{877}$

Step 3

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

$A = 8$

$B = 90$

$C = 82$

$a = 30$

$b = 5 \sqrt{877}$

$c = 145$