Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
Question
Chapter 73, Problem 1A
To determine

(a)

Thelength of diagonal AB.

Expert Solution
Check Mark

Answer to Problem 1A

The length of diagonal AB is AB=82.61mm

Explanation of Solution

Given information:

The dimensions of rectangular solid block are

  AC=31.50mmCD=24.75mmBD=72.25mm

  Mathematics for Machine Technology, Chapter 73, Problem 1A , additional homework tip  1

Calculation:

To calculate the length of diagonal AB, the length of side BC is required. Let us consider the triangle BDC, the angle D of the triangle is a right-angle, so the triangle BDC is a right-angle triangle.

In triangle BDC, the length of side BC can be calculated from Pythagorean theorem.

  BC2=BD2+DC2BC2=(72.25)2+(24.75)2BC2=5832.625BC=5832.625BC=76.37mm

Let us consider the triangle ABC, the angle C of the triangle is a right-angle, so the triangle ABC is a right-angle triangle.

In triangle ABC, the length of side AB can be calculated from Pythagorean theorem.

  AB2=BC2+AC2AB2=(76.37)2+(31.50)2AB2=6824.875AB=6824.875

  AB=82.61mm

Conclusion:

Thus, the true length of diagonal AB is AB=1.897in.

To determine

(b)

The value of CAB.

Expert Solution
Check Mark

Answer to Problem 1A

The value of CAB is CAB=67.58°.

Explanation of Solution

Given information:

The given figure is

The dimensions of rectangular solid block are

  AC=31.50mmCD=24.75mmBD=72.25mm

  Mathematics for Machine Technology, Chapter 73, Problem 1A , additional homework tip  2

Calculation:

Let us consider the triangle ABC, the angle C of the triangle is a right-angle, so the triangle ABC is a right-angle triangle.

In triangle ABC,

  tanCAB=BCAC=76.37( 31.50)CAB=tan1(2.424)

  CAB=67.5855°

  CAB=67.58°

Conclusion:

Thus, the value of CAB is CAB=67.58°.

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