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Law of Sines? (Book error?)?
Solve the triangle:
a = 40, b = 30, A = 75°
I got B = 46.423°, C = 75.58°, and c = 40.11
My book says differently, and I really think it made an error... They got C = 134°, and consequently that c = 29.7886.
They got C by subtracting 46° from 180°, but doesn't A + B + C = 180°, not C + B = 180°? I'm reluctant to think the book published a mistake, but it seems like a simple human error of leaving an angle out...
Opps, you guys are right, I made an error too. I got 75.58 from putting "180 - 46.423 + 75" into my calculator. Should have used parentheses or a minus sign. :P We all make mistakes~
C = 58.577
6 Answers
- Jeff AaronLv 79 years ago
If A = 75 then C can't be 134, because that adds up to more than 180.
But your numbers have the same problem: 75 + 46.423 + 75.58 > 180
You were right about B, it's approximately 46.423.
That means that C is approximately 58.577.
- ?Lv 79 years ago
If C = 134° and A = 75° then A + C = 209°
..and as the sum of angles in a triangle is 180° (and we haven't included B yet) then that's a pretty good reason to think the book is wrong.
- HermanLv 59 years ago
If A was 75°, how could C possible be 134° ?! A + C alone would be higher than 180°! There is no way the book can be right!
- DaveWHLv 79 years ago
I agree with Herman.
B = 46.4 and if A = 75 then angle C = 180 - (75 + 46.4) = 58.6, so an answer of 134 degrees for C can't possibly be right.
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- Anonymous9 years ago
herman is right.
book must be wrong.
