Explanation Formula used: The law of sines: For any triangle A B C , the laws of sines are a sin A = b sin B = c sin C . The law of sines can also be expressed as, sin A a = sin B b = sin C c . Calculation: Given that a = 29.4 cm , b = 40.8 cm , A = 42.7 ° . Evaluate the other two angles by using law of sines as follows. a sin A = b sin B 29.4 sin 42.7 ° = 40.8 sin B 29.4 0.6781 = 40.8 sin B 43.3564 sin B = 40.8 Simplify further as follows. sin B = 0.94103 B ≈ 70.2 ° Thus, ∠ B = 70.2 ° . Another possible value for B is ∠ B = 180 ° − 70.2 ° = 109.8 ° . Note that the sum of three angles in a triangle is 180 ° . Therefore, evaluate the measure of ∠ C as follows. ∠ A + ∠ B + ∠ C = 180 ° 42.7 ° + 70.2 ° + ∠ C = 180 ° ( ∵ ∠ B = 70.2 ° ) ∠ C = 180 ° − 112.9 ° ∠ C = 67.1 ° Thus, ∠ C = 67.1 ° . Evaluate another possible measure of ∠ C as follows. ∠ A + ∠ B + ∠ C = 180 ° 42

Pearson eText Algebra and Trigonometry: Graphs and Models -- Instant Access (Pearson+)

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Author: Marvin Bittinger, Judith Beecher

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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Pearson eText Algebra and Trigonometry: Graphs and Models -- Instant Access (Pearson+)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The Δ A B C if a = 29.4 cm , b = 40.8 cm , A = 42.7 ° .

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