Law of sines for ASA and AAS

Law of sines for ASA and AAS triangles

Learn to solve nonambiguous triangles when two angles and one side are known. This precalculus practice set develops correct opposite-side pairing, the angle-sum check, exact side calculations and a surveying application. It also explains why three angles determine a shape without determining its scale.

Single-select and multiselect questions progress from the sine-law relationship to complete deductions from ASA and AAS information. Explanations show which side belongs with each angle, use an altitude to justify the relationship and check whether the given measurements can describe a nondegenerate triangle.

Practice guidance

Label the vertices and opposite sides before calculating. Find the third angle, select a known side-angle pair and keep full calculator precision until the final requested rounding. Exact questions need no calculator; the surveying item explicitly permits a scientific calculator in degree mode. This set focuses on uniquely determined ASA and AAS data. The separate SSA practice set handles the possibility of zero, one or two triangles.