Questions: Use the Law of Sines or the Law of Cosines to solve each triangle. Round all angle measures to the nearest tenth of a degrees and side Given? SSS Use: Law of Cosines Triangle B= degrees C= degrees

Use the Law of Sines or the Law of Cosines to solve each triangle. Round all angle measures to the nearest tenth of a degrees and side Given? SSS Use: Law of Cosines Triangle B= degrees C= degrees
Transcript text: Use the Law of Sines or the Law of Cosines to solve each triangle. Round all angle measures to the nearest tenth of a degrees and side Given? SSS Use: Law of Cosines Triangle B= degrees C= degrees
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Solution

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Solution Steps

Step 1: Find angle B using the Law of Cosines

We are given a triangle with sides a = 8 in, b = 18 in, and c = 12 in. We can use the Law of Cosines to find angle B. b² = a² + c² - 2ac * cos(B) 18² = 8² + 12² - 2 * 8 * 12 * cos(B) 324 = 64 + 144 - 192 * cos(B) 324 = 208 - 192 * cos(B) 116 = -192 * cos(B) cos(B) = -116/192 B = arccos(-116/192) B ≈ 127.2°

Step 2: Find angle C using the Law of Cosines

c² = a² + b² - 2ab * cos(C) 12² = 8² + 18² - 2 * 8 * 18 * cos(C) 144 = 64 + 324 - 288 * cos(C) 144 = 388 - 288 * cos(C) -244 = -288 * cos(C) cos(C) = 244/288 C = arccos(244/288) C ≈ 32.1°

Step 3: Find angle A using the fact that the sum of angles in a triangle is 180°

A + B + C = 180° A + 127.2° + 32.1° = 180° A + 159.3° = 180° A = 180° - 159.3° A ≈ 20.7°

Final Answer:

  • B ≈ 127.2°
  • C ≈ 32.1°
  • A ≈ 20.7°
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