Explanation Formula used: The law of cosines: For any triangle A B C , the laws of cosines are, 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. Calculation: Solving a triangle means finding the lengths of all its sides and the measures of all its angles. The known measures are a = 23.4 ft, b = 15.7 ft and c = 8.3 ft and the unknown measures are ∠ A = ? , ∠ B = ? , ∠ C = ? . Substitute a = 23.4 ft, b = 15.7 ft and c = 8.3 ft in a 2 = b 2 + c 2 − 2 b c cos A . a 2 = b 2 + c 2 − 2 b c cos A ( 23.4 ) 2 = ( 15.7 ) 2 + ( 8.3 ) 2 − 2 ( 15.7 ) ( 8.3 ) cos A ( Substituting ) 547.56 = 246.49 + 68.89 − 260.62 cos A 260.62 cos A = − 232.18 Simplify further as follows. cos A = − 232.18 260.62 cos A = − 0

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ISBN: 9780134383385

Author: Penna

Publisher: VST

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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, Problem 7RE

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