<math><mstyle displaystyle="true"><mtable class="shapeTable" columnlines="solid" rowlines="solid"><mtr><mtd><mi>Side</mi></mtd><mtd><mi>Angle</mi></mtd></mtr><mtr><mtd><mtable><mtr><mtd><mrow><mi>b</mi><mo>=</mo></mrow></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mrow><mi>c</mi><mo>=</mo></mrow></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mrow><mi>a</mi><mo>=</mo></mrow></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mtd><mtd><mtable><mtr><mtd><mrow><mi>A</mi><mo>=</mo></mrow></mtd><mtd></mtd></mtr><mtr><mtd><mrow><mi>B</mi><mo>=</mo></mrow></mtd><mtd></mtd></mtr><mtr><mtd><mrow><mi>C</mi><mo>=</mo></mrow></mtd><mtd></mtd></mtr></mtable></mtd></mtr></mtable></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>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>2</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>4</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>32</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>28</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>32</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>28</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>32</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</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>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>4</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>16</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>20</mn></mstyle></math> .

Simplify the denominator.

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

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</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>28.95502437</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>75.52248781</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>104.47751218</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>104.47751218</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 tri{4}{}{4}{}{2}{}? 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 four hundred eleven million two hundred fifty-six thousand five hundred sixty-two |
---|

- 1411256562 has 16 divisors, whose sum is
**2823292992** - The reverse of 1411256562 is
**2656521141** - Previous prime number is
**3847**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 33
- Digital Root 6

Name | eight hundred ninety-four million nine hundred forty-three thousand four hundred seventy-seven |
---|

- 894943477 has 4 divisors, whose sum is
**915756160** - The reverse of 894943477 is
**774349498** - Previous prime number is
**43**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 55
- Digital Root 1

Name | two billion one hundred one million four hundred seventy-six thousand two hundred sixty-seven |
---|

- 2101476267 has 64 divisors, whose sum is
**2846638080** - The reverse of 2101476267 is
**7626741012** - Previous prime number is
**11**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 36
- Digital Root 9