12th Edition

ISBN: 9780358403685

Author: Larson

Publisher: HM CC

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Question

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 10.1, Problem 3C

To determine

To find the angle measures of the given triangle and classify the triangle

Expert Solution & Answer

Answer to Problem 3C

The angles measures are 27,45,108 respectively.

The triangle is a scalene triangle.

Explanation of Solution

Given information:

Ratio of the angle measures in a triangle is given as 3:5:12

Calculation:

Let the angle measures be 3x, 5x, 12x.

The sum of all the angles of a triangle is 180. Hence,

3x+5x+12x=180∘

Adding all the x on the left side of the equation

20x=180∘

Divide both the sides by 20

20x20=18020

This will give the value of x=9

Hence the angle measures are

First angle is 3x ,multiply3 with 9

x=3×9 ,get x=27

Second angle 5x ,multiply 5 with 9

x=5×9 ,get x=45

Third angle is 12x ,multiply12 with 9

x=12×9 ,get x=108

As all the angle measures are different, which implies that all the sides of the triangle are of different lengths. Hence the triangle is Scalene triangle.

Conclusion- The angle measures of the triangle are 27,45,108 and the triangle can be classified as Scalene triangle.

Chapter 10.1, Problem 2C

Chapter 10.1, Problem 1E

Chapter 10 Solutions

EBK PRE-ALGEBRA

Ch. 10.1 - Prob. 1C Ch. 10.1 - Prob. 2C Ch. 10.1 - Prob. 3C Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E

Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.2 - Prob. 1C Ch. 10.2 - Prob. 2C Ch. 10.2 - Prob. 3C Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - 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