Mathematics Trigonometry

Properties of trianglesSin Rule- In ΔABC a, b, c are sides opposite to angles A, B, C then sine rule for triangle is-Proof- A In ΔABC, draw ADBC Now in ΔADB,D = 90 Also B D cFrom (1) and (2), We get— Similarly we can prove hence ProvedExamples- In ΔABC If Solution In ΔABC Now we know thatansExample2- If side AB and BC of a are 3 and 4 and then find other parts.Solution- we know that and b= , Hence Now, so A=Other parts A= ansExample 3-An angle A in the triangle ABC is 45o, that angle B is 30o and that the length b is 2 units. Can you work out the remaining angle C and the lengths a and c? Solution- we know that