CLASS 10 · LEARNING KNOWLEDGE
General triangles and areas
How it works
For general triangles, the law of cosines connects two sides and the included angle with the third side. The trigonometric area formula uses the same included angle.
Note
c²=a²+b²−2ab·cos γ; A=a·b·sin γ/2.
c²=a²+b²−2ab·cos γ; A=a·b·sin γ/2.
An example
A triangle has sides a=10 cm and b=8 cm with included angle γ=120°. Calculate the third side. Round to two decimal places. Give the result in cm.
Cosine rule: c=√(10²+8²−2·10·8·cos(120°)). Result: 15.62 cm.
Try it yourself now
50 Exercises · three difficulty levels · selection and number input
To the learning unit →Own explanation and own practice exercises by AmyMath. Subject reference framework: KMK Educational Standards Mathematics ESA/MSA. The topic assignment may vary by federal state.