Understand the Sine and Cosine Rules
This assumes you already have a knowledge of basic trigonometry(ir using sin, cos and tan in a right angled triangle, if you don’t click here to read my lesson on these) and aims to teach you how to use the sine and cosine rule.
In basic trigonometry you can only look at a right angled triangle which greatly limits its applications, however with these formula you can calculate sides and angles in any triangle provided you know enough information. They are proved by splitting one triangle in 1/2 so that the dividing line is perpendicular to one of the sides and therefore creating 2 right angled triangle in which the normal rules can be applied.
The following use symbols as defined in the above triangle. Note that side a is opposite angle A and b is opposite B etc
a/sinA = b/sinB = c/sinC
This allows us to find both an angle and a side as we can invert all of the fractions and it remains true. This means if we know the side opposite the angle we want and any other side angle pair we can work out the angle we want, or we can work out a side if we know the angle opposite it and any other side angle pair.
a = 10cm
b = 5cm
B = 30o
and we want to find angle A
we know a side angle pair, b and B, and we know the side opposite the angle we want so we can write the sine rule as
sinA / 10 = sinB/b >>note we don’t need to include the c parts as we dont know either c or C
sinA / 10 = sin30/5
sinA = 10sin30/5
sinA = 1
A = sin-11
A = 90o
We can work out any angle or side in a similar way.
This rule allows us to find an angle if we know all the sides or a side if we know the other 2 and a angle
c² = a² + b² – 2abcosC
To find an angle we can re-arrange it so
C = cos-1((a2 + b2 – c2)/2ab)
Im sure you can put the numbers in yourself as ive show you how it can be written to find either an angle or side so ill leave you to it enjoy