Question

Consider a triangle like the one below. Suppose that C=128 degrees, a=66 , and b=15. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

Answer 1

To solve the triangle, use the Law of Sines and the Law of Cosines. Find angle A using the Law of Sines, side c using the Law of Cosines, and the remaining angle B using the sum of angles formula.

Step-by-step explanation:

To solve the triangle, we can use the Law of Sines and the Law of Cosines. First, we can use the Law of Sines to find angle A:

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

sin(A) / 66 = sin(128) / 15

Solving for A, we find A ≈ 30.1°. Next, we can use the Law of Cosines to find side c:

c^2 = a^2 + b^2 - 2ab * cos(C)

c^2 = 66^2 + 15^2 - 2(66)(15) * cos(128)

Solving for c, we find c ≈ 48.7. Finally, we can use the remaining side and angle to find the remaining angle:

B = 180 - A - C

B = 180 - 30.1 - 128

Solving for B, we find B ≈ 21.2°.