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

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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=abc4AAreaoftriangleA=s(sa)(sb)(sc)Perimeteroftriangles=a+b+c2

Given:

The triangle has angles measuring 30,30and120 if the measures of congruent side 6 units each.

Calculation:

The angle measures of a triangle are 30,30and120 suppose the measures of congruent side 6 units each.

Here, the angles are 30,30and120. 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(1202)=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,andc=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(11.19510.39)(11.1956)(11.1956)=11.195(0.805)(5.195)(5.195)=243.22A=15.5

Therefore,

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