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>76</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>118</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>118</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>a</mi></mstyle></math> .

Factor each term.

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

Evaluate <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>62</mn><mo>)</mo></mrow></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0.88294759</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

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

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

Multiply each term in <math><mstyle displaystyle="true"><mfrac><mrow><mn>0.6691306</mn></mrow><mrow><mi>a</mi></mrow></mfrac><mo>=</mo><mn>0.07357896</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

Rewrite the equation as <math><mstyle displaystyle="true"><mn>0.07357896</mn><mi>a</mi><mo>=</mo><mn>0.6691306</mn></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>0.07357896</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>0.07357896</mn><mi>a</mi><mo>=</mo><mn>0.6691306</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.07357896</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>0.07357896</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0.6691306</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.07357896</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>b</mi></mstyle></math> .

Factor each term.

Evaluate <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>76</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>9.09404741</mn></mstyle></math> .

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

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

Multiply each term in <math><mstyle displaystyle="true"><mfrac><mrow><mn>0.97029572</mn></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mn>0.07357896</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

Rewrite the equation as <math><mstyle displaystyle="true"><mn>0.07357896</mn><mi>b</mi><mo>=</mo><mn>0.97029572</mn></mstyle></math> .

Divide each term by <math><mstyle displaystyle="true"><mn>0.07357896</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>0.07357896</mn><mi>b</mi><mo>=</mo><mn>0.97029572</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.07357896</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>0.07357896</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0.97029572</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.07357896</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 , B=76 , c=12? 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.