   Chapter 11.CR, Problem 27CR 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

In Review Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit.Each of the legs of an isosceles triangle is 40 cm is length. The base is 30 cm in length. Find the measure of a base angle.

To determine

The measure of the base angle of an isosceles triangle which has its legs of length 40 cm and base 30 cm.

Explanation

Procedure used:

In any triangle ABC such that

AB=c,

BC=a,

CA=b,

mA=α,

mB=β, and

mC=γ.

The Law of cosines is given by

a2=b2+c2-2bccosα

b2=c2+a2-2cacosβ

c2=a2+b2-2abcosγ

The Law of sines is given by

asinα=bsinβ=csinγ

Calculation:

Given:

Length of the legs of an isosceles triangle =40 cm

The length of the base =30 cm

Thus,

Assume that ABC is the isosceles triangle with

AB=BC=40 cm, and

AC=30 cm.

Take,

a=40 cm

b=30 cm, and

c=40 cm

Also, mBAC=α (say)

Now, apply the law of cosines in the triangle ABC

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