Solve the triangle . b = 8; a = 3; b = 8; c = 7; a - 3; c = 7 B A= boxed 53.13 ^ (Do not round until the final answer. Then round to the nearest degree as needed.) B= boxed 22.62 ^ ( Do not round until the final answer. Then round to the nearest degree as needed.) C= boxed 104.25 ^ o ( Do not round until the final answer. Then round to the nearest degree as needed.)
To solve the triangle, we can use the Law of Cosines to find angle B first:
cos(B) = (a^2 + c^2 - b^2) / (2ac)
cos(B) = (3^2 + 7^2 - 8^2) / (2*3*7)
cos(B) = (9 + 49 - 64) / 42
cos(B) = (58 - 64) / 42
cos(B) = -6 / 42
cos(B) = -0.142857
B = cos^(-1)(-0.142857)
B ≈ 98.13 degrees
Now, we can find angle A using the fact that the sum of the angles in a triangle is 180 degrees:
A = 180 - B - C
A = 180 - 98.13 - 104.25
A ≈ 77.62 degrees
Therefore, the triangle is:
A = 77.62 degrees
B = 98.13 degrees
C = 104.25 degrees