Explanation Calculation: Consider the corner of the triangle, A = 3 , 2 , B = − 4 , − 1 and C = 1 , 0 Note that the slope of the line joining the points x 1 , y 1 and x 2 , y 2 is given by, m = y 2 − y 1 x 2 − x 1 Therefore, the slope of the line joining the points A 3 , 2 and C 1 , 0 is: m 1 = 0 − 2 1 − 3 = − 2 − 2 = 1 The slope of the line joining the points B − 4 , − 1 and C 1 , 0 is: m 2 = 0 − − 1 1 − − 4 = 1 5 The slope of the line joining the points B − 4 , − 1 and A 3 , 2 is: m 3 = 2 − − 1 3 − − 4 = 3 7 Therefore, the slopes of the side of the triangle are 1 , 1 5 and 3 7 , respectively. If m 1 , m 2 be the slopes of two lines, then the angle between them is: tan θ = m − 2 m 1 1 + m 1 m 2 The angle between sides AC and BC at point 1 , 0 is: tan θ 1 = 1 − 1 5 1 + 1 1 5 = 4 5 6 5 = 2 3 Solve for θ 1 , θ 1 = 33

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.1, Problem 57E

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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Chapter 6.1, Problem 56E

Chapter 6.1, Problem 58E

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Chapter 6 Solutions

Trigonometry (MindTap Course List)

Chapter 6.1, Problem 1ECP Chapter 6.1, Problem 2ECP Chapter 6.1, Problem 3ECP Chapter 6.1, Problem 4ECP Chapter 6.1, Problem 5ECP Chapter 6.1, Problem 1E Chapter 6.1, Problem 2E Chapter 6.1, Problem 3E Chapter 6.1, Problem 4E Chapter 6.1, Problem 5E

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Chapter 6.1, Problem 57E

Solution Summary: The author calculates the slopes of each side of the triangle, and uses them to find the measure of interior angle.

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