Basic Trig Identities: You only can use basic trig when there is a triangle with a right angle and the necessary information.
There needs to be a right triangle because there needs to be an hypothenuse. Furthermore basic trig consists of Sine, Cosine and Tangent, which is also SOH, CAH, TOA. A trick used to know what side (opposite, adjacent, hypothenuse) of the triangle is needed to figure out the angle (vice versa).
Look at this example……. We knew the angle F (38*) and the side FD (10 cm), which is also the hypothenuse. Meaning that we can use the formula CAH to figure out the side ‘d’. We put the given numbers into the equation, rearranged it and then we were left with the answer (7.9 cm) to the adjacent side of COS 38*.
Sine Law Identities: You can only use sine law if you have a non right triangle and atlas on of the angles and their opposing side of the triangle.
The sine law equation looks like this… Sin A / a = Sin B / b = Sin C / c …. Meaning that the angle of A divided by its opposing side (side a) is equal to angle of B (or C) divided by opposing side b (or side c).
Take in this example….. It is NOT a right triangle but we do know the angle of G and its opposing side g or known as JH (10 cm). We also know side h or known as GJ (15 cm) but what we do not know is angle H. So what we can do is punch all our given answers into the above sine law equation, rearrange it, to then come to our answer which we will invert sine it, to finally get the real answer of angle H (34*).
Cosine Law Identities: Cosine law can be used for any type of triangle but ONLY ones that have a contained angle and information limited enough, that it is impossible to use the sine law.
The Cosine law equation looks like this…. c*2 = a*2 + b*2 – (2ab cosC) ….. This equations is used if there is not a given answer for an angle AND its opposing side length, because with that information you can use sine law. However, without it, you need to use cosine.
Look at this example…. Immediately we can see that there is a contained angle (an angle that is “cornered” by a length of a side on both sides of it). We can also notice that there is limited information, so the sine law will not work and it is NOT a right triangle so the basic trig will not work either. Therefore we will take the oscine equations up above and bunch our given information into the equation and we will come out with out finally answer (6.3 cm).
In grade 10 I only knew the basic trig identities, which were useful but if it was not given enough information or if it was NOT a right triangle I would have to do so much extra work (ex/ splitting the triangle into two). Though, now in grade 11, with the sine and cosine law, I do not have to do as much work as before because I have the knowledge to do steps that I did not know how to do before.