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>53</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>43</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>1849</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2809</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5184</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1849</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>7993</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>53</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>106</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>6144</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>7632</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6144</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>7632</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>128</mn></mrow><mrow><mn>159</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>43</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>53</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>2809</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1849</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5184</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2809</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>7033</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>43</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>86</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4224</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>6192</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4224</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6192</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>88</mn></mrow><mrow><mn>129</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>36.3867076</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>46.98650937</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>83.37321698</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>83.37321698</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=43 , b=53 , 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 | nine hundred one million three hundred ninety-three thousand four hundred seventy |
---|

- 901393470 has 32 divisors, whose sum is
**2884459392** - The reverse of 901393470 is
**074393109** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 36
- Digital Root 9

Name | nine hundred sixty-two million four hundred fifteen thousand eight hundred thirty-two |
---|

- 962415832 has 128 divisors, whose sum is
**4057454592** - The reverse of 962415832 is
**238514269** - Previous prime number is
**31**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 40
- Digital Root 4

Name | one billion four hundred twelve million seven hundred eighty-six thousand five hundred twenty-one |
---|

- 1412786521 has 4 divisors, whose sum is
**1417608612** - The reverse of 1412786521 is
**1256872141** - Previous prime number is
**293**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 37
- Digital Root 1