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3 years ago

Find the unknown sides and angles of this triangle using the Law of Cosines. Round to the nearest hundredth.

Mathematics

1 answer:

Svetlanka [38]3 years ago

3 0

Answer:

Side c = 10.35

Angle A = 50.87°

Angle B = 94.13°

Step-by-step explanation:

The Law of Cosines states that:

a² = b² + c² - 2bcCos A

We are to to find side c, Angle A and B

side a = 14

sides b = 18

Angle C = 35°

1) Side c

= c² = a² + b² - 2abCos C

c² = 14² + 18² - 2 × 14 × 18 Cos 35

c = √(14² + 18² - 2 × 14 × 18 Cos 35)

c = 10.3512

Approximately = 10.35

2) Angle A

Cos A = b² + c² - a²/2bc

A = arc cos (b² + c² - a²/2bc)

A = arc cos (18² + 10.35² - 14²/2 × 18 × 10.35)

A = 50.8737°

A = Approximately = 50.87°

3) Angle B

Cos B = a² + c² - b²/2ac

B = arc cos (a² + c² - b²/2ac)

B = arc cos (14² + 10.35² - 18²/2 × 14× 10.35)

A = 94.13123°

A = Approximately = 94.13°

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