Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 73, Problem 53AR
To determine

The angle x.

Expert Solution & Answer
Check Mark

Answer to Problem 53AR

The angle is 114°12.

Explanation of Solution

Given:

Angle shown in below figure:

Mathematics For Machine Technology, Chapter 73, Problem 53AR , additional homework tip  1

Calculation:

Mathematics For Machine Technology, Chapter 73, Problem 53AR , additional homework tip  2

Apply cos rule in triangle ABC as follows:

  cosA=b2+c2a22bccos28°= ( 5.2 )2+ ( 8.3 )2a22×5.2×8.3a=4.44

So, the side BC=4.44.

Apply sine rule intriangle ABC as follows:

  sinABC=sinBACsin28°4.44=sinB5.2sinB=0.5498B=33.355°

Angle BCA is calculated as follows:

  BCA+33.355°+28°=180°BCA=118.6445°

Angle ABC is calculated as follows:

  ABC+33.355°=93°ABC=59.645°

Apply cos rule in triangle ABC as follows:

  cosB=a2+c2b22accos59.645°= ( 4.44 )2+ ( 9.1 )2 ( A C )22×4.44×9.1AC=7.85409

Apply sine rule intriangle ABC as follows:

  sinABC=sinBACsinA4.44=sin59.645°7.85409A=29.1968°

Angle BCA is calculated as follows:

  BCA+59.645°+29.1968°=180°BCA=91.158°

Angle ACD is calculated as follows:

  ACD+91.158°+118.6445°=260°ACD=50.1975°

Apply sine rule intriangle ACD as follows:

  sinDAC=sinCADsinD7.85409=sin50.1975°8D=48.9593°

Angle DAC is calculated as follows:

  DAC+48.9593°+50.1975°=180°DAC=80.843°

Angle x is calculated as follows:

  x=DAC+BACx=80.843°+33.355°x=114.198°x=114°12

Thus, the angle is 114°12.

Conclusion:

The angle is 114°12.

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Chapter 73 Solutions

Mathematics For Machine Technology

Ch. 73 - Prob. 11ARCh. 73 - Prob. 12ARCh. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in decimal degree to 2...Ch. 73 - Determine the values A in decimal degree to 2...Ch. 73 - Determine the values A in decimal degree to 2...Ch. 73 - For each of the following functions of angles,...Ch. 73 - For each of the following functions of angles,...Ch. 73 - For each of the following functions of angles,...Ch. 73 - For each of the following functions of angles,...Ch. 73 - Solve the following exercises. Compute angles to...Ch. 73 - Solve the following exercises. Compute angles to...Ch. 73 - Solve the following exercises. Compute angles to...Ch. 73 - Prob. 29ARCh. 73 - Prob. 30ARCh. 73 - Prob. 31ARCh. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Prob. 40ARCh. 73 - Prob. 41ARCh. 73 - Prob. 42ARCh. 73 - Prob. 43ARCh. 73 - Prob. 44ARCh. 73 - Prob. 45ARCh. 73 - Prob. 46ARCh. 73 - Prob. 47ARCh. 73 - Prob. 48ARCh. 73 - Prob. 49ARCh. 73 - Determine the sine, cosine, tangent, cotangent,...Ch. 73 - Determine the sine, cosine, tangent, cotangent,...Ch. 73 - Prob. 52ARCh. 73 - Prob. 53ARCh. 73 - Determine the sine, cosine, tangent, cotangent,...Ch. 73 - Prob. 55ARCh. 73 - Prob. 56AR
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