I am very new to maths so I would appreciate if posters are patient with me as this is a learning curve
I have a triangle with no equal sides and I am looking to find angle B. The length of the sides I will make up as 12cm, 22cm and 28cm.
I know all three sides and none of the angles and I am thinking that I should be using the cosine rule, therefore I have completed the following;
C2 = a2 + b2 – 2ab cos Ø
122 = 222 + 282 – 2 · 22 · 28 cos Ø
144 = 484 + 784 – 1232 cos Ø
144 = 1268 – 1232 cos Ø
1232 cos Ø = 1124
Cos Ø = 1124
1232
Cos Ø = 0.91
Cos -1 Ø = 24.2º (1dp)
Have I used the right rule, if not please advise why, and if I have would you please advise why I can't use the Sine Rule and what the difference is?
Thanks
David
Looking deeper into this today it seems that I am using the wrong cosine rule?
The book in the summary section only shows; c^2 = a^2 + b^2 - 2ab cos C
I initially thought the book print had make an error where I thought that cos C should have read cos theta, which is what I then wrote on this forum.
Using;
b^2 = c^2 + a^2 - 2ac cos B
angle B =
28^2 = 12^2 + 22^2 - 2 x 22 x 12 cos B
784 = 144 + 484 - 328 cos B
- 528 cos B = 784 - 628
= 156 / 528
cos B = 0.29
theta = cos -1 (0.29) = 73 degrees.
This is what I think is right, any views welcome
David
Your right, the conclusion I get using the formula you wrote is 107 degrees?
Now I am even more confused
David
Edited section below;
I have had another look at the formula I used here;
b^2 = c^2 + a^2 - 2ac cos B
I can see in my transposition that I changed the negative sign to a positive when changing the integers from side to side because I thought ending up with a negative - 0.29 was incorrect, however after working out the angle I do indeed get 107 degrees, which is what I also get when using the formula as you wrote it, which I might add is a tidy method and proves that a less chance of making the mistake I made possible.
I think we can agree now that the solution is 107 degrees and I do like the way you do the formula, which is better than in my maths book.
Thanks
David