Question

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A-22, C - 51.4%, c-2.69 B=____ a=______ b=_______

Answer 1

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles, respectively.

We are given A, C, and c, so we can use the Law of Sines to find B, a, and b.

a/sin(A) = c/sin(C)

a/sin(22) = 2.69/sin(51.4)

a = sin(22) * (2.69/sin(51.4))

a = 1.00

b/sin(B) = c/sin(C)

b/sin(B) = 2.69/sin(51.4)

b = sin(B) * (2.69/sin(51.4))

We can use the fact that the sum of the angles in a triangle is 180 degrees to find B:

B = 180 - A - C

B = 180 - 22 - 51.4

B = 106.6

Now we can substitute the values we have found into the Law of Sines to find b:

a/sin(A) = b/sin(B)

1/sin(22) = b/sin(106.6)

b = sin(106.6) * (1/sin(22))

b = 2.69

Therefore, B is approximately 106.6 degrees, a is approximately 1.00, and b is approximately 2.69.