   Chapter 11.CR, Problem 11CR 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 9 to 12, use the Law of Sines or the Law of cosines to find the indicated length of side or angle measure. Angle measures should be found to the nearest degree; distances should be found to the nearest tenth of a unit. To determine

To find:

The indicated length of side or angle measure using the law of sines or the Law of cosines.

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:

From the above figure we have

a=y,

c=20,

α=40°, and

β=60°

By the law of sine we have

asinα=bsinβ=csinγ

Let us find the value of γ by the angle sum property of a triangle. In any triangle, the sum of the all the three angles is 180°

(i.e

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