Question

Solve the triangle. Round all answers to two decimal places. 36 38 RECEN b 76° = B Recall the following formulas: b sin (A) sin(B) sin(C) a² = b² + c² - 2bc cos (A) a​

Answer 1

Answers:

angle C = 68°

side a = 24.09

side b = 39.77

The decimal values are approximate.

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Work Shown

A+B+C = 180°

C = 180° - A - B

C = 180° - 36° - 76°

C = 68°

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Law of Sines

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

a/sin(A) = c/sin(C)

a/sin(36°) = 38/sin(68°)

a = sin(36°)*(38/sin(68°))

a = 24.089979

a = 24.09

Please make sure your calculator is set to degrees mode.

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Law of Sines

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

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

b/sin(76°) = 38/sin(68°)

b = sin(76°)*38/sin(68°)

b = 39.766911

b = 39.77

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The fully solved triangle has these sides:

• a = 24.09 (approximate)
• b = 39.77 (approximate)
• c = 38

And it has these angles:

• A = 36°
• B = 76°
• C = 68°

I used GeoGebra to verify the answers.

See the diagram below.