   Chapter 11.4, Problem 6E 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 Exercises 5 and 6, state the form of the Law of Cosines used to solve the problem. Using the values provided, give the answer in a form such as a 2 = b 2 + c 2 − 2 a b   cos α . See the figure for Exercises 1 to 8.a) Find b if it is known that a = 5.7 ,   c = 8.2  and  β = 79 ∘ .b) Find β if it is known that a = 6 ,   b = 8 ,  and  c = 9 . Exercises 1-8

To determine

a.

To Find:

The side of b by Law of Cosines.

Explanation

Formula:

The Law of Cosines

a2=b2+c22bccosα

b2=a2+c22accosβ

c2=a2+b22abcosγ

Where α, β, and γ is the acute angle of the triangle, and a, b, and c is the sides of the triangle.

Calculation:

Given:

In ABC

a=5.7

c=8.2 and

β=79

By the Law of Cosines:

b2=a2+c22accosβ

Substitute a=5

To determine

b.

To Find:

The angle of β by using the Law of Cosines.

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