This is the pattern that solves each of #1, #2
1) Compute sin(A) / a.
2) Compute sin(B) = [(b * sin(A)) / a]
3) Compute B by taking the inverse sine of sin(B)
4) Knowing the two angles A and B, subtract their sum from 180 degrees to find C.
5) Compute sin(C) - easy
6) Since:
sin(C).....sin(A)
--------- = ---------
...c...........a
7) a * sin(C) = c * sin(A)
8) c = ((a * sin(C)) / sin(A))
9) Since you already know a, sin(A), and sin(C) this is nothing but arithmetic.
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1) Since (sin(58) / 11) = 0.07710, (sin(B) / 12.8) = 0.07110.
So: sin(B) = (12.8) * 0.07110 = 0.98682. Take the inverse sine of this to find the angle B = 80.68720 degrees.
We know that the sum of the angles of a triangle is 180 degrees, so C = 180 - (58 + 80.68720) = 180 - 138.68720 = 41.31280 degrees.
Since we know that sin(C) / c = 0.07110 and that sin(C) = 0.66017. So:
0.66017 / c = 0.07110.....Multiply both sides by c
(0.66017) = (0.07110) * c.....Divide both sides by 0.07110
c = (0.66017 / 0.07110) = 9.28508
Summarizing - with angles in degrees
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A = 58, B = 80.68720, C = 41.31280
a = 11, b = 12.8, c = 9.28508
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Now that you have the steps and an example to follow #2 is easy. I'll leave that one for you to do so that you'll learn it and not just another read another identical type of problem.
(I'm an ex-teacher - you know how it is - I want you to learn how to do these so that when your exam comes up you will have solved one of them.) E-mail me if you get stuck. But I'm sure that you can handle this one easily.
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3) This requires the law of cosines.
b^2 = a^2 + c^2 - 2ac*cos(B)
Since B = 8.25 degrees, cos(B) = 0.98965
So b^2 = 26^2 + 18^2 - (2 * 26 * 18 * 0.98965) =
676 + 324 - 926.31370 = 1000 - 926.31370 = 73.68630
b = sqrt(b^2) = 8.58407
Now we know sin(B) / b = (0.14349 / 8.58407) = .01672
So sin(C) / c = sin(A) / a = 0.01672
So (sin(C) / 18) = 0.01672......Multiply both sides by 18, getting:
sin(C) = 0.30089 and taking the inverse sine, C = 17.51111 degrees
Since A + B + C = 180 degrees, A = (180 - 8.25 - 17.51111) =
A = 154.23889 degrees
Summarizing - with all angles in degrees
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A = 154.23889, B = 8.25, C = 17.5111
a = 26, b = 8.58407, c = 18
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