Solving triangles
Solve a triangle in four cases: a side and two angles, two sides and the angle between them, three sides, and two sides with an angle opposite one of them. Section: Grade 9, solving any triangle; right triangles are in the Grade 8 studio.
- Germany: grade 10
- Ukraine: grade 9
- Russia: grade 9
Guide
In Ukrainian Grade 9 geometry (§4) to solve a triangle means to find the unknown sides and angles from the known ones. The sides are a, b and c and the angles opposite to them are α, β and γ.
There are four main cases. A side and two angles: find the third angle first, then the other sides by the sine rule. Two sides and the angle between them: find the third side by the cosine rule. Three sides: find the angles by the cosine rule.
With two sides and an angle opposite one of them, sometimes two different triangles can be drawn. This happens because a sine value belongs to two angles: an acute one and an obtuse one.
Write the solution as Given, Find, Solution, Answer. Take sine and cosine values from a calculator and round to tenths.
The triangle is drawn to scale: 1 square on the board is 1 cm.