b^2 = a^2 + c^2 - 2ac cos 54 = 1485
b = 38.5
Check your numbers again.
I get sinA = a*sinB/b = .1366
A = 7.85 degrees
B=54deg a=42 c=6.5
1. I found length of b using law of cosine and got 36.2
2. Using side of b, I used the law of sine to get angle A = 28.2
3. I added B+A and subtracted from 180 to get angle C = 127.8 which DOES NOT make sense since side c is the smallest side. I can't seem to find my error. Help please?
Thanks
b = 38.5
Check your numbers again.
I get sinA = a*sinB/b = .1366
A = 7.85 degrees
I got 61.8deg for A this time... which would make C have 64.2deg which still doesn't make sense...
1. You correctly used the Law of Cosines to find the length of side b. Given that a = 42, c = 6.5, and B = 54 degrees, you can use the formula:
b² = a² + c² - 2ac * cos(B)
Plugging in the values,
b² = 42² + 6.5² - 2 * 42 * 6.5 * cos(54)
b² = 1764 + 42.25 - 546 * 0.5878
b² ≈ 1845.57
Taking the square root, b ≈ 42.9 (rounded to the nearest tenth).
2. Now, let's find angle A. We can use the Law of Sines to relate the sides and angles:
sin(A) / a = sin(B) / b
Plugging in the values,
sin(A) / 42 ≈ sin(54) / 42.9
Rearranging the equation and solving for sin(A),
sin(A) ≈ (sin(54) / 42.9) * 42
sin(A) ≈ 0.80902
Now, we can take the inverse sine to find A,
A ≈ arcsin(0.80902)
A ≈ 53.2 (rounded to the nearest tenth).
3. Finally, to find angle C, we can use the fact that the sum of angles in a triangle is 180 degrees:
C = 180 - A - B
C = 180 - 53.2 - 54
C ≈ 72.8 (rounded to the nearest tenth).
Therefore, the correct answer is:
A ≈ 53.2 degrees
B ≈ 54 degrees
C ≈ 72.8 degrees
If you double-check your calculations using these steps, it should help you identify the error you made.