Question

Solve for the unknown measure of A in 31^2 = 27^2 + 22^2 – 2(27)(22) cos A.

Answer 1

First, isolate cos A by itself.
Subtracted both sides by (27^2 + 22^2) and divide by 2(27)(22).
Use calculator to get cos A=7/33

Answer 2

Correction: dvide both sides by -2(27)(22)

Answer 3

Now, I'm thinking that this is from a triangle using Law of Cosine.
Then, angle A has to be between 0 and pi/2.

Answer 4

Now, solve cos A=7/33 over 0 and pi/2 to get A=arccos(7/33) (Unit is radians)
Decimal form is 1.3577051269... radians.
In degree, A is about 77.75331027 degrees.

Answer 5

To me, the number of the left hand side forms the form of (27-22)^2 = 5^2 =25
therefore, cos A = 31^2/25 = 38.44 --> no solution because cos of angle cannot be > 1

Answer 6

oh sorry, right hand side, not left hand side
@ybarrap what do you think?

Answer 7

Now, 27^2 + 22^2 – 2(27)(22) cos A is not (27-22)^2

Answer 8

because there is cos A multiplied to -2(27)(22)
If it were 27^2+22^2-2(27)(22), then you would be right.

Answer 9

oh yea, you are right, I am sorry. misread the problem.

Answer 10

My bad. :) I am sorry

Answer 11

That's alright.
Sometimes, I make stupid mistakes, too.

Answer 12

Here's just another way to look at this problem...
$$
a\bullet b=|a||b|\cos A=31^2 = 27^2 + 22^2 – 2(27)(22) \cos A\\
\implies \\
a=27\\
b=22\\
\implies
A=\cos^{-1}\cfrac{31^2}{27\times22}
$$

Answer 13

That's another way to look at it.

Answer 14

@ybarrap I don't get!!

Answer 15

He used the "vector version" of the Law of Cosine

Answer 16

http://en.wikipedia.org/wiki/Law_of_cosines

Answer 17

got it, thanks.

Answer 18

Master is master, junior is junior. hehehe. wait for me , Master

Answer 19

I just happened to see the form, not always obvious

Answer 20

I learn so much from you @Loser66 and everyone else here, even these problems give me practice and it reinforces my knowledge