Question

Find the exact value of the trig functions of angle B. Rationalize denominators as needed.

a = 6 , C = 7 please include steps.

Answer 1

To find the trigonometric functions of angle B, use the Law of Cosines and Law of Sines to find the angles and sides of the triangle.

Step-by-step explanation:

To find the trigonometric functions of angle B, we need to use the known values of a = 6 and C = 7. First, let's find angle A using the Law of Cosines:

1. c^2 = a^2 + b^2 - 2ab * cos(C)
2. b^2 = c^2 - a^2 - 2ab * cos(C)
3. b = sqrt(c^2 - a^2 - 2ab * cos(C))
4. b = sqrt(7^2 - 6^2 - 2 * 7 * 6 * cos(110°))
5. b ≈ 3.29

Now that we have angle A and side b, we can find angle B using the Law of Sines:

1. a/sin(A) = b/sin(B)
2. 6/sin(A) = 3.29/sin(B)
3. sin(B) = (sin(A) * 3.29) / 6
4. B ≈ 20.96°

Finally, we can find the trigonometric functions of angle B:

• sin(B) ≈ sin(20.96°)
• cos(B) ≈ cos(20.96°)
• tan(B) ≈ tan(20.96°)