Solve the equation for 0 degrees< a < 90 degrees
(3.3^2) = (5.1^2) + (8.1^2) - 2(5.1)(8.1)cos a
Very brief explanation would be awesome
+23254 Yep, the answer is 12.3°.
I forgot to check my answer. With cosine, you get two possible answers, the answer that the calculator gives you plus another answer, its supplement.
So, if you take 180° - 167.7°, you get 12.3°.
Why should you know that you need to take the supplement?
Well, if the answer is 167.7°, it is a very large (obtuse) angle, and the side opposite it must be the largest side in the triangle; it must be very large when compared to the other two sides. It isn't -- in fact, it's the shortest side, so angle A must be the smallest angle. Then, you need to subract your answer from 180°.
OK now?
+23254 This looks as if you are using the Law of Cosines:
(3.3^2) = (5.1^2) + (8.1^2) - 2(5.1)(8.1)cos(A)
I would first calculate the numbers:
10.89 = 26.01 + 65.61 - 82.62cos(A)
10,89 = 91.62 - 82.62cos(A)
Subtract 91.62 from both sides (do NOT combine it with the -82.62!)
-80.73 = 82.62cos(A)
Divide both sides by 82.62:
-0.977124 = cos(A)
To get the size of the angle, find invCos(-0.977124), which is 167.7°
If you have any questions about any of the steps, please ask.
The answer is 12.3
I got the same answer as you but I can't seem to figure out how the answer is 12.3
Do you know how to get to 12.3
+23254 Yep, the answer is 12.3°.
I forgot to check my answer. With cosine, you get two possible answers, the answer that the calculator gives you plus another answer, its supplement.
So, if you take 180° - 167.7°, you get 12.3°.
Why should you know that you need to take the supplement?
Well, if the answer is 167.7°, it is a very large (obtuse) angle, and the side opposite it must be the largest side in the triangle; it must be very large when compared to the other two sides. It isn't -- in fact, it's the shortest side, so angle A must be the smallest angle. Then, you need to subract your answer from 180°.
OK now?
