Solve a triangle from two sides and their included angle. Beside solved sas triangle, the output shows the operation used to obtain it.
The law of cosines extends the Pythagorean theorem by adding the included-angle term −2ab cos C.
Sides 7 and 9 with included angle 60° produce the opposite side and the remaining two angles.
Solve the opposite side first, then use an inverse cosine or sine check for the remaining angles. Law of Cosines also connects to angle-rich triangle.
The entered angle must be between the two entered sides. Using a nonincluded angle describes a different triangle.
Law of Cosines uses Side a, Side b, and Included angle C in degrees. Check that all three angles total 180° and that the longest recovered side faces the largest angle.
For this law of cosines result, preserve which angle faces each side and keep every length unit consistent through the final step.
SAS triangles, diagonal distances, resultant vectors, and non-right geometry use this relationship. Law of Cosines also relates to SAS area.
Read Solved SAS triangle against Side a, not in isolation. Use Side b to estimate the Law of Cosines magnitude. When Included angle C in degrees is altered, label the new Law of Cosines trial. Its Solved SAS triangle should not replace the original Law of Cosines answer.
A round value for Side a gives Law of Cosines a quick boundary test. Leave Side b fixed, predict Solved SAS triangle, and compare that prediction with the new Law of Cosines output. A disagreement identifies a specific part of the Law of Cosines setup to inspect.
Delay rounding Solved SAS triangle until the next Law of Cosines step is clear. Preserve enough digits to test the relationship with Side a. Final precision should reflect Side b, not merely the calculator display.
The law of cosines extends the Pythagorean theorem by adding the included-angle term −2ab cos C.
SAS triangles, diagonal distances, resultant vectors, and non-right geometry use this relationship.
The entered angle must be between the two entered sides. Using a nonincluded angle describes a different triangle.