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10 POINTS!!! Label the sides of the triangle (a, b, and c). Use the Law of Cosines and the Law of Sines to solve the triangle. Round your answer to the nearest whole number.

10 POINTS!!! Label the sides of the triangle (a, b, and c). Use the Law of Cosines-example-1
User Pirxpilot
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1 Answer

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Answer:

c = 29, A = 48°, B = 54°

Explanation:

The unknown side is c. Using the last Law of Cosines formula, we find it to be ...

c² = a² +b² -2ab·cos(C)

c² = 22² +24² -2(22)(24)cos(78°) ≈ 840.445

c ≈ √840.445 ≈ 29 . . . . . rounded to integer

__

The angle at B can be found using the Law of Sines. We want the angle in the numerator, so we can write the equation as ...

sin(B)/b = sin(C)/c

B = arcsin(b/c·sin(C)) ≈ arcsin(24/28.9904×sin(78°))

B ≈ 54°

The remaining angle can be found using the sum of angles of a triangle:

A +B +C = 180°

A = 180° -B -C = 180° -54° -78° = 48°

The solution to the triangle is ...

c = 29, A = 48°, B = 54°

10 POINTS!!! Label the sides of the triangle (a, b, and c). Use the Law of Cosines-example-1
User Artina
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