   Chapter 11.CR, Problem 15CR 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 length of the sides of a rhombus are 6 in. each and the longer diagonal measures 11 in. Find the measure of each of the acute angles of the rhombus.

To determine

To find:

The measure of each of the acute angles of the rhombus.

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:

The length of each side of a rhombus =6 in.

The length of the longer diagonal =11 in.

Let ABCD be the rhombus with diagonals AC and BD, which intersect at ‘O’.

From the above figure we have

AB=BC=CD=DA=6 in.

AC=11 in.

First consider the triangle ABC to find the mABC by the application of the cosine formula.

Thus, in ABC wee have

AB=6 in.,

BC=6 in., and

AC=11 in.

Let mABC=α

Now, apply the law of cosine in ABC by taking

AC=11 in. =a,

BC=6 in. =b,

AB=6 in. =c, and

mABC=α

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