Unit 7 · Core unit
Triangles that are not right-angled, and the inverse functions that recover an angle. Choosing the correct law from the given parts is most of the work.
What a strong answer looks like
A strong answer names the configuration first, because SAS and ASA point to different laws before any computation.
Know
Two angles with a side is an angle-side pair and points to the Law of Sines. Two sides with the included angle, or three sides, points to the Law of Cosines.
Apply
Identify the configuration, then apply the matching law.
Watch out
Reaching for the Law of Cosines when only one side is known, where it cannot start.
Study move
Classify four triangle configurations and name the law for each.
Know
Two sides and a non-included angle can produce two triangles, one, or none, depending on the height compared with the given side.
Apply
Compute both candidate angles and test whether each leaves a valid third angle.
Watch out
Keeping only the calculator principal angle and missing the second triangle.
Study move
Work an SSA case that yields two valid triangles.
Know
Inverse functions return principal values from restricted ranges, not every angle with that value.
Apply
Report the principal value, then find any other required angle from symmetry.
Watch out
Assuming the inverse returns the angle you had in mind rather than the principal one.
Study move
State the principal value of an inverse and the other angle sharing that value in one turn.
Modeling drill
A surveyor measures a 100-metre baseline with angles of 40 and 65 degrees to a landmark. Find the distance and name the law used.
