   Chapter 11.CR, Problem 16CR 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 13 to 17, use the Law of S i n e s or the Law of C o s i n e s to solve each problem. Angle measures should be found to the nearest degree; distances should be found to the nearest tenth of a unit.The area of △ A B C is 9.7 in2. If a = 6 in. and c = 4 in., find the measure of angle B.

To determine

To find:

The measure of angle B

Explanation

Procedure used:

In any triangle ABC such that

AB=c,

BC=a,

CA=b,

mA=α,

mB=β, and

mC=γ.

For the above triangle the area is given by

A=12 acsinβ

Calculation:

Given:

The area of ABC=9.7 in2.

Two of the sides of the triangle are a=6 in., and c=4 in.

The above triangle can be represented diagrammatically as

For the above triangle the area is given by

A=12 acsinβ.

Substitute; a=6 in., c=4 in., and A=9.7 in2. In the above equation,

9.7=1264sinβ

9

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