Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 55, Problem 20A

Solve the following exercises based on Principles 11-14, although an exercise may require the application of two or more of any of the principles. Round the answers to 3 decimal places where necessary unless otherwise stated.
a. If A B = 5.378 " and A C = 3.782 " , find (1) DB (2) A C B .

b If D B = 3.017 " and A C B = 7.308 " , find (1) AB (2) C B .

Chapter 55, Problem 20A, Solve the following exercises based on Principles 11-14, although an exercise may require the

Expert Solution
Check Mark
To determine

(a)

The value of DB and arc ACB.

Answer to Problem 20A

The value of DB is DB=2.689.

Explanation of Solution

Given information:

AB = 5.378"

  AC=3.782"

  Mathematics For Machine Technology, Chapter 55, Problem 20A , additional homework tip  1

If the radius of the circle is perpendicular to the chord, it always divides the chord in two equal parts.

In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB.

  AD=DB=AB2

  DB=AB2=5.3782=2.689DB=2.689

The value of DB is DB=2.689

If the radius of the circle is perpendicular to the chord, it always divides the chord and the arc cut off by the chord in two equal parts.

In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB. Also, the arc cut off by the chord is divided in two equal parts.

  AC=CB=ACB2

  AC=CB= ACB2AC=3.782"ACB=2×3.782"=7.564"ACB=7.564"

The value of DB is DB=2.689 and the value of arc is ACB=7.564".

Conclusion:

Thus, the value of DB is DB=2.689 and the value of arc is ACB=7.564".

Expert Solution
Check Mark
To determine

(b)

The value of AB and arc CB.

Answer to Problem 20A

The value of AB is AB=6.034" and the value of arc is CB=3.654".

Explanation of Solution

Given information:

AB = 3.017"

  ACB=7.308"

  Mathematics For Machine Technology, Chapter 55, Problem 20A , additional homework tip  2

If the radius of the circle is perpendicular to the chord, it always divides the chord in two equal parts.

In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB.

  AD=DB=AB2

  AB=2×DBAB=2×3.017"AB=6.034"

The value of AB is AB=6.034"

If the radius of the circle is perpendicular to the chord, it always divides the chord and the arc cut off by the chord in two equal parts.

In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB. Also, the arc cut off by the chord is divided in two equal parts.

  AC=CB=ACB2

  AC=CB= ACB2ACB=7.308"CB=7.308"2CB=3.654"

The value of AB is AB=6.034" and the value of arc is CB=3.654"

Conclusion:

Thus, the value of AB is AB=6.034" and the value of arc is CB=3.654".

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