The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.

Substitute the known values into the law of sines to find <math><mstyle displaystyle="true"><mi>B</mi></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mn>42</mn><mo>)</mo></mrow></mrow><mrow><mn>26</mn></mrow></mfrac></mstyle></math> .

Evaluate <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>42</mn><mo>)</mo></mrow></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0.6691306</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>26</mn></mstyle></math> .

Multiply both sides of the equation by <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> .

Simplify both sides of the equation.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.02573579</mn></mstyle></math> .

Take the inverse sine of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>B</mi></mstyle></math> from inside the sine.

Evaluate <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mn>0.46324426</mn><mo>)</mo></mrow></mstyle></math> .

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the second quadrant.

Subtract <math><mstyle displaystyle="true"><mn>27.59665301</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

The solution to the equation <math><mstyle displaystyle="true"><mi>B</mi><mo>=</mo><mn>27.59665301</mn></mstyle></math> .

Exclude the invalid angle.

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>42</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>27.59665301</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>69.59665301</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>69.59665301</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.

Substitute the known values into the law of sines to find <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Factor each term.

Evaluate <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>110.40334698</mn><mo>)</mo></mrow></mstyle></math> .

Evaluate <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>42</mn><mo>)</mo></mrow></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0.6691306</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>26</mn></mstyle></math> .

Solve for <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Multiply each term by <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and simplify.

Multiply each term in <math><mstyle displaystyle="true"><mfrac><mrow><mn>0.93726162</mn></mrow><mrow><mi>c</mi></mrow></mfrac><mo>=</mo><mn>0.02573579</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Rewrite the equation as <math><mstyle displaystyle="true"><mn>0.02573579</mn><mi>c</mi><mo>=</mo><mn>0.93726162</mn></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>0.02573579</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>0.02573579</mn><mi>c</mi><mo>=</mo><mn>0.93726162</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.02573579</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>0.02573579</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0.93726162</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.02573579</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=42 , a=26 , b=18? 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 ninety-eight million six hundred eighty-three thousand nine hundred twenty-two |
---|

- 1798683922 has 16 divisors, whose sum is
**2793987072** - The reverse of 1798683922 is
**2293868971** - Previous prime number is
**92687**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 55
- Digital Root 1

Name | two hundred five million seven hundred forty-seven thousand nine hundred eighty-three |
---|

- 205747983 has 8 divisors, whose sum is
**209584128** - The reverse of 205747983 is
**389747502** - Previous prime number is
**383**

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

Name | one billion one hundred ninety million six hundred sixty-six thousand six hundred sixty-two |
---|

- 1190666662 has 16 divisors, whose sum is
**1845021312** - The reverse of 1190666662 is
**2666660911** - Previous prime number is
**1453**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7