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>120</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>85</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>100</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>10000</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>14400</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>7225</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>10000</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>21625</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>120</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>240</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>85</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>11625</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>20400</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>75</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>11625</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>75</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>20400</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>155</mn></mrow><mrow><mn>272</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>100</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>85</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>120</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>14400</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>10000</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>7225</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>14400</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>17225</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>200</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>85</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2825</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>17000</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2825</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>17000</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>113</mn></mrow><mrow><mn>680</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>55.26002846</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>80.43441514</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>135.69444361</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>135.69444361</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=100 , b=120 , c=85? 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 | six hundred forty-nine million seven hundred five thousand sixty-eight |
---|

- 649705068 has 32 divisors, whose sum is
**1676661120** - The reverse of 649705068 is
**860507946** - Previous prime number is
**31**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | one billion eight hundred fourteen million two hundred eleven thousand six hundred thirty-five |
---|

- 1814211635 has 8 divisors, whose sum is
**2182740480** - The reverse of 1814211635 is
**5361124181** - Previous prime number is
**383**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 32
- Digital Root 5

Name | seven hundred seventy million fifty-four thousand nine hundred sixty-six |
---|

- 770054966 has 4 divisors, whose sum is
**1155082452** - The reverse of 770054966 is
**669450077** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 44
- Digital Root 8