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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 7.2, Problem 26E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
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Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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A triangle has angles measuring 30 ∘ , 30 ∘ , and 120 ∘ . If the congruent sides measure 6 units each, find the length of the radius of the circumscribed circle.

To determine

To find:

The length of the radius of the circumscribed circle.

Explanation

Formula used:

Radius of circumscribed circle:

Let a, b,c and c denote the triangle’s three sides and A denote the area of the triangle. Then the radius of the circumscribed of the triangle is

R=abc4AArea of triangle A=s(s−a)(s−b)(s−c)Perimeter of triangle s=a+b+c2

Given:

The triangle has angles measuring 30∘,30∘ and 120∘ if the measures of congruent side 6 units each.

Calculation:

The angle measures of a triangle are 30∘,30∘ and 120∘ suppose the measures of congruent side 6 units each.

Here, the angles are 30∘,30∘ and 120∘. One of the angles is more than 90∘ so, it is a obtuse triangle.

We sketch the figure of the triangle of the circumscribed circle.

By the above figure we take sides measures b=6, c=6.

Next we find the triangle side ‘a’

a=2b sin(A2)          =2(6) sin(120∘2)         =12 sin 60∘        =12(32)       =63       =6(1.732)a=10.39   (approximately)

We find the perimeter of the triangle,

Substituting the values a=10.39, b=6, and c=6 in perimeter of triangle formula,

s=10.39+6+62   =22.392s=11.195

Then we find area of the triangle,

A=11.195(11.195−10.39)(11.195−6)(11.195−6)     =11.195(0.805)(5.195)(5.195)     =243.22A=15.5

Therefore,

Radius   of  the circumcenter R=(10.39)(6)(6)4(15

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Sect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10E
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