Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 76, Problem 13A
To determine

(a)

The sketch and label of a rectangular solid.

Expert Solution
Check Mark

Answer to Problem 13A

The sketch and label of a rectangular is shown in Figure-(1).

Explanation of Solution

Project auxiliary lines that form right triangles containing the given angles, the axis of the hole, and the angles to be computed, R and T. BC is a side of ΔBCD, which contains the given 19°00 angle. BC is also a side of right ΔBCE, which contains R that is to be computed.

The sketch and label of a rectangular is shown below.

Mathematics For Machine Technology, Chapter 76, Problem 13A

Figure-(1)

To determine

(b)

The angle of rotation R.

Expert Solution
Check Mark

Answer to Problem 13A

The angle of rotation R is 30°49.

Explanation of Solution

Write the expression for the angle D using the triangle BCD.

  tanD=BCDC ...... (I)

Here, the length of the side BC is BC and the length of the side DC is DC.

Write the expression for the angle A using triangle ACE.

  tanA=CEAE ...... (II)

Here, the length of the side CE is CE and the length of the side AE is AE.

Write the expression for the angle R using triangle BCE.

  tanR=BCCE ...... (III)

Calculation:

Consider the length of the side BC is equal to 1unit.

Substitute 1unit for BC and tan19°00 for tanD in Equation (I).

  tan19°00=1unitDCDC=1unittan19°00DC=1unit0.3443DC=2.9042unit

The length of the side AE and DC are same. Therefore, the length of the side AE is 2.9042unit.

  AE=2.9042unit

Substitute 2.9042unit for AE and 30°00 for A in Equation (II).

  tan30°00=CE2.9042unitCE=(2.9042unit)tan30°00CE=(2.9042unit)(0.5773)CE=1.6767unit

Substitute 1.6767unit for CE and 1unit for BC in Equation (III).

  tanR=1unit1.6767unittanR=0.5964R=tan1(0.5964)R=30°49

Conclusion:

The angle R is 30°49.

To determine

(c)

The angle of tilt C.

Expert Solution
Check Mark

Answer to Problem 13A

The angle of tilt T is 33°54.

Explanation of Solution

Write the expression for the length BE using the triangle BCE.

  BE=BC2+CE2 ...... (IV)

Write the expression for the angle T using triangle AEB.

  tanT=BEAE ...... (V)

Calculation:

Substitute 1unit for BC and 1.6767unit for CE in Equation (IV).

  BE= ( 1unit )2+ ( 1.6767unit )2= ( 3.8113unit )2=1.9522unit

Substitute 1.9522unit for BE and 2.9042unit for AE in Equation (V).

  tanT=1.9522unit2.9042unittanT=0.6721T=tan1(0.6721)T=33°54

Conclusion:

The angle T is 33°54.

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