Question

Solve the triangle using the Law of Sines. (Assume b = 6, ∠A = 50°, and ∠C = 110°. Round the lengths to two decimal places.)

a = ??
c = ??
∠B = ??

Answer 1

a ≈ 10.21, c ≈ 11.68, and ∠B ≈ 20°

Explanation:

To use the Law of Sines, we need to know either two angles and one side or two sides and one non-included angle. In this case, we are given two angles (A and C) and one side (b). We can use the fact that the sum of the angles in a triangle is 180° to find the third angle:

∠B = 180° - ∠A - ∠C

∠B = 180° - 50° - 110°

∠B = 20°

Now we can use the Law of Sines to find the other two sides:

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

a / sin(50°) = 6 / sin(20°)

a = sin(50°) * (6 / sin(20°))

a ≈ 10.21

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

c / sin(110°) = 6 / sin(20°)

c = sin(110°) * (6 / sin(20°))

c ≈ 11.68

Therefore, a ≈ 10.21, c ≈ 11.68, and ∠B ≈ 20°.

Answer 2

here u go mate
everything on paper