Kari Lilica
My teacher may have passed me in Trigonometry, but I cannot accept it because I still don't fully understand the above mentioned...
I really need help cause reading alone isn't helping... @_@
I need someone to explain it to me! xP
Thanks in advance!
If you want a specific problem, I don't know when to apply a Law on a given problem D:
Especially the Law of Cosines >.<
But I think I better start with the Law of Sines
Oh ok, so for the law of sines and the law of cosines we typically letter the variables as follows. Each of the sides are given a small letter, a,b, c and the angles that are opposite the sides are given the corresponding big letter. A is the angle across from side a, B is the angle across from side b, and C is the angle across from side c.
The law of sines is as follows.
a/sin(A) = b/sin(B) = c/sin(C)
so if your given 2 sides (lets say a and b) and one corresponding angle (lets say A) then you can easily find the second corresponding angle, which in our example would be angle B. You just use your calculator and algebra to do the rest. Also similarly given 2 angles and 1 corresponding side, you can find the 2nd corresponding side.
The law of cosines is as follows.
c^2 = a^2 + b^2 - (2ab)cos(C)
it should be realized that when angle C is 90 degrees
c^2 = a^2 + b^2 - (2ab)cos(90)
but cos(90)=0
so you get
c^2 = a^2 + b^2
the Pythagorean theorem
so essentially our equation is adjusted slightly to accommodate any triangle, whether or not it is right
c^2 = a^2 + b^2 - (2ab)cos(C)
Since now there is no hypotenuse, a,b and c, are arbitrarily labeled on the sides. So it's easy to see the following equations are true.
b^2 = a^2 + c^2 - (2ac)cos(B)
a^2 = b^2 + c^2 - (2bc)cos(A)
So lets sum this up in words, if you have 2 sides (lets say a and b) and an angle that is not corresponding to either of those angles (lets say angle C), you can find the side that is corresponding to that angle (side c) using this formula. Also of you have the 3 sides given to you (a, b, c), you can find anyone of the angles by using a little algebra. It should be noticed that law of sines can't be used to solve either of these situations. If fact, the law of cosines can also be used if your given 2 sides (lets say a and b) and a corresponding angle (lets say angle B) and find the remaining side (side c) using a little algebra. However the law of sines is a lot easier to use, since it requires less algebra. The only case that you can only use the law of sines is when your given 2 angles and a corresponding side.
Let me know if you have more questions, or a practical example that we can work on.
