Law of cosines for SAS and SSS

Law of cosines for SAS and SSS triangles

Practise solving triangles from two sides and their included angle, or from all three side lengths. This precalculus set develops the cosine law from coordinate geometry and applies it to exact side calculations, angle reconstruction, navigation and checks on whether a triangle can exist.

Single-select and multiselect items progress from derivation and method selection to applications where a turning angle must be distinguished from the triangle’s interior angle. Explanations connect the largest side with the largest angle, distinguish acute, right and obtuse triangles, and retain enough precision for a reliable final answer.

How to approach the problems

Check positive lengths and strict triangle inequalities before using inverse cosine. For SAS, identify the angle between the two known sides. For SSS, reconstruct an angle with the rearranged cosine law and check its range. Exact answers are used where practical; calculator items state degree mode and rounding. This practice complements the sine-law sets and treats each question as an independent problem.