Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

Solve the equation.

Substitute the known values into the equation.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>67</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>60</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3600</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4489</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5184</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3600</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>9673</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>67</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>134</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> .

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>6073</mn></mrow><mrow><mn>9648</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

Solve the equation.

Substitute the known values into the equation.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>60</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>67</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4489</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>3600</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5184</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>4489</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>8784</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>60</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>120</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4295</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>8640</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4295</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8640</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>859</mn></mrow><mrow><mn>1728</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The sum of all the angles in a triangle is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees.

Add <math><mstyle displaystyle="true"><mn>50.98993634</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>60.19124971</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>C</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>111.18118606</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>111.18118606</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

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

Do you know how to Solve the Triangle a=60 , b=67 , c=72? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion seven hundred forty-seven million four hundred thirty-one thousand three hundred ninety-five |
---|

- 1747431395 has 16 divisors, whose sum is
**2173482720** - The reverse of 1747431395 is
**5931347471** - Previous prime number is
**521**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 44
- Digital Root 8

Name | one billion two hundred ninety-four million five hundred eighty-six thousand six hundred seventy |
---|

- 1294586670 has 64 divisors, whose sum is
**3358200384** - The reverse of 1294586670 is
**0766854921** - Previous prime number is
**281**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | four million three hundred twenty-two thousand eight hundred five |
---|

- 4322805 has 16 divisors, whose sum is
**6990144** - The reverse of 4322805 is
**5082234** - Previous prime number is
**97**

- Is Prime? no
- Number parity odd
- Number length 7
- Sum of Digits 24
- Digital Root 6