Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 70, Problem 42A
To determine

The distance x.

Expert Solution & Answer
Check Mark

Answer to Problem 42A

The distance x is 1.041in.

Explanation of Solution

The below figure represent the schematic diagram of the system.

  Mathematics for Machine Technology, Chapter 70, Problem 42A

       Figure -(1)

Write the expression of cosine rule in ΔADC for the angle ADC.

cosADC=AC2AD2DC22(AD)(DC) ......... (I)

Here, the sides of ΔADC is AD,DCandAC respectively.

Write the expression for the relation between angles in ΔADC.

ACD=CAD ...... (II)

Write the expression of sum of angles in ΔADC .

ACD+CAD+ADC=180°CAD+CAD+ADC=180°2CAD+ADC=180° ...... (III)

Write the expression of DAB.

DAB=BACCAD ...... (IV)

Write the expression for the relation between angles in ΔABD.

DAB=DBA ...... (V)

Write the expression of ADB.

ADB=180°DABDBA=180°DABDAB=180°2DAB ...... (VI)

Write the expression of cosine rule in ΔADB.

AB2=AD2+AB22(AD)(AB)cosADB ......... (VII)

Calculation:

Substitute 40° for ADC, 0.750in for AD, 0.750in for DC in Equation (I).

cos40°=AC2 ( 0.750in )2 ( 0.750in )22( 0.750in)( 0.750in)AC2(0.750in)2(0.750in)2=(0.8618 in2)AC2=0.2632in2AC=0.513in

Substitute 40° for ADC in Equation (III).

2CAD+40°=180°2CAD=180°40°CAD=140°2CAD=70°

Substitute 116° for BAC and 70° for CAD in Equation (IV).

DAB=116°70°=46°

Substitute 46° for DAB in Equation (VI).

ADB=180°2(46°)=180°92°=88°

Substitute x for AB, 88° for DAB, 0.750in for AD, 0.750in for AB in Equation (VII).

x2=(0.750in)2+(0.750in)22(0.750in)(0.750in)cos88°x2=1.0857in2x=1.0857 in2x=1.041in

Conclusion:

The distance x is 1.041in.

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Chapter 70 Solutions

Mathematics for Machine Technology

Ch. 70 - Find x. All dimensions are in inches.Ch. 70 - Prob. 12ACh. 70 - Find x. All dimensions are in inches.Ch. 70 - Find x. All dimensions are in inches.Ch. 70 - Find side x. All dimensions are in millimeters.Ch. 70 - Two sides and an angle opposite one of the sides...Ch. 70 - Two sides and an angle opposite one of the sides...Ch. 70 - A 21-mm side, 29-mm side, a 41 angle opposite the...Ch. 70 - A 0.943" side, a 0.612" side, and a 6215' angle...Ch. 70 - A 2.10-ft side, a 3.05-ft side, a 2930' angle...Ch. 70 - A 16.35-mm side, a 23.86-mm side, a 115 angle...Ch. 70 - An 87.60-mm side, a 124.80-mm side, a 12.90 angle...Ch. 70 - A 34.090" side, a 35.120" side, a 4618' angle...Ch. 70 - Solve the following exercises using the Law of...Ch. 70 - Solve the following exercises using the Law of...Ch. 70 - Solve the following exercises using the Law of...Ch. 70 - Solve the following exercises using the Law of...Ch. 70 - Solve the following exercises using the Law of...Ch. 70 - Solve the following exercises using the Law of...Ch. 70 - Find x. All dimensions are in inches.Ch. 70 - Find side x. All dimensions are in millimeters.Ch. 70 - Find side x. All dimensions are in inchesCh. 70 - Solve the following exercises using a combination...Ch. 70 - Solve the following exercises using a combination...Ch. 70 - Solve the following exercises using a combination...Ch. 70 - Prob. 36ACh. 70 - Solve the following exercises using a combination...Ch. 70 - Solve the following exercises using a combination...Ch. 70 - Solve the following machine shop exercises. Find...Ch. 70 - Solve the following machine shop exercises. Find...Ch. 70 - Prob. 41ACh. 70 - Prob. 42ACh. 70 - Solve the following machine shop exercises. Find...Ch. 70 - Solve the following machine shop exercises. Find...Ch. 70 - Prob. 45ACh. 70 - Solve the following machine shop exercises. Find...Ch. 70 - Prob. 47ACh. 70 - Prob. 48A
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