In this week of pre calc we were working on Trigonometry. We learned Sine Law and Cosine Law and where we should use them.
Sine Law: a/sinA=b/sinB=c/sinC or sinA/a=sinB/b=sinC/c
For using sine law in the questions we should know that first of all we only can use two of the fractions and second of all for solving the equation we should know three thing from the triangle (either 2 angles and a side or 2 sides and an angle) to be able to solve the equation. We can use sine law in the questions which has an angle and the opposite side. In that case we can use sine law for solving.
After finding an angle by using the sine law we should pay attention that there is a possibility which our question can have 2 answers. because the sine in the unit circle is positive in either quadrant 1 and quadrant 2. but our calculator only give us the angle in quadrant 1. We should check the angle in quadrant 2 because in some cases that’s the answer either.
Cosine Law: a² = b²+ c² -2bc.cosA , b² = a² + c² -2ac.cosB , c² = a² + b² -2ab.cosC
We can use cosine law when we want to find the third side of a triangle when we know 2 sides and the angle between them or the angle of a triangle when we know all the 3 sides. In the second case we should rearrange the original formula which will be ;
cosA = b2 + c2 − a² / 2bc , cosB = a² + c² – b² / 2ac , cosC = a² + b² – c² / 2ab