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

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
3 views

# 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:

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,

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### solve the equation by using the quadratic formula. 140. 2x2 + 7x 15 = 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### 57. If find y’.

Mathematical Applications for the Management, Life, and Social Sciences

#### Simplify the expressions in Exercises 97106. 32/331/6

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Using tan2 x = sec2 x − 1, ∫ tan3 x dx =

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 