Explanation Formula used: The law of cosines: In any triangle A B C , a 2 = b 2 + c 2 − 2 b c cos A b 2 = a 2 + c 2 − 2 a c cos B c 2 = a 2 + b 2 − 2 a b cos C Thus, in any triangle, the square of a side is the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle. When the included angle is 90 ° , the law of cosines reduces to the Pythagorean theorem. The law of cosines can also be expressed as, cos A = b 2 + c 2 − a 2 2 b c cos B = a 2 + c 2 − b 2 2 a c cos C = a 2 + b 2 − c 2 2 a b Calculation: Solving a triangle means finding the lengths of all its sides and the measures of all its angles. The known measures are a = 15 , c = 7 , B = 62 ° and the unknown measures are ∠ A = ? , ∠ C = ? , b = ? . The given triangle falls under the situation SAS. Thus, law of cosines should be used to solve the triangle. Substitute a = 15 , c = 7 , B = 62 ° in b 2 = a 2 + c 2 − 2 a c cos B . b 2 = a 2 + c 2 − 2 a c cos B = ( 15 ) 2 + ( 7 ) 2 − 2 ( 15 ) ( 7 ) cos 62 ° ( Substituting ) = 225 + 49 − 210 ( 0

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

6th Edition

ISBN: 9780136880172

Author: Marvin Bittinger, Judith Beecher

Publisher: PEARSON+

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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°).

Chapter 8.2, Problem 18E

To determine

The law which applies for the given triangle and to solve the given triangle.

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Chapter 8.2, Problem 17E

Chapter 8.2, Problem 19E

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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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