   Chapter 11.CR, Problem 17CR 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.Find the area of the rhombus in Exercise 15.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 area of the rhombus.

Explanation

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.

Substitute; the above values in the Law of cosines,

a2=b2+c2-2bccosα

(11)2=62+62-266cosα

121=36+36-72cosα

121=72-72cosα

Add; -7 2 on both side,

121+-72=72-72cosα+-72

By the associative property of addition we have

121+-72=72-72+-72cosα

49=-72cosα

Divide by -72 on both side,

49-72=-72cosα-72

-0

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