   Chapter 11.CT, Problem 16CT 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

On the basis of the drawing provided, complete the Law of Sines. sin ⁡ α a = _________ To determine

To complete:

The law of sine using the drawing given.

Explanation

Given:

The Law of Sines.

Theorem:

In any acute triangle, the three ratios between the sines of the angles and the lengths of the opposite sides are equal and is given by sinαa=sin βb=sinγc or asinα=bsin β=csinγ, which is called the Law of Sines.

Calculation:

From the area formulas,

A=12bcsinα=12casinβ=12absinγ

Multiplying the areas by 2, we get

bcsinα=casinβ=absinγ

Dividing by abc, we get

bcsin⁡</

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