Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth. If B = 150°, a = 150 ft, c = 30 ft, find b.

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asked Aug 28, 2023 142k views

4 votes

Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth.

If B = 150°, a = 150 ft, c = 30 ft, find b.

Mathematics
high-school

PrathapG asked

by PrathapG

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1 Answer

5 votes

Answer: 176.6

Work Shown:

$b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 150^2 + 30^2 - 2*150*30*\cos(150)\\\\b^2 \approx 31194.22863406\\\\b \approx √(31194.22863406)\\\\b \approx 176.618879608211\\\\b \approx 176.6\\\\$