Chapter 69, Problem 8A

Determine the height of gage blocks required to set the angles in Exercises 7 and 8 on a 10" sine plate.
a. 44°20'
b. 0°20'
c. 2°26'
d. 19°51'
e. 25°31'

To determine

(a)

Find the height of gage blocks required to set the angle ${44}^{\circ }{20}^{\text{'}}$ on a ${10}^{"}$ sine plate.

Answer to Problem 8A

Height of the gage blocks: $=6.9883\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a 10" sine plate is ${44}^{\circ }{20}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${44}^{\circ }{20}^{\text{'}}$ on a ${10}^{"}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=10\text{'}\text{'}\times \sin {44}^{\circ }{20}^{\text{'}}\\ h=10\text{'}\text{'}\times \sin {44.333}^{\circ }\\ \Rightarrow h=6.9883\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=6.9883\text{'}\text{'}$

To determine

(b)

Find the height of gage blocks required to set the angle $0^{\circ }{20}^{\text{'}}$ on a ${10}^{"}$ sine plate.

Answer to Problem 8A

Height of the gage blocks: $=0.0582\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a 10" sine plate is $0^{\circ }{20}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle $0^{\circ }{20}^{\text{'}}$ on a ${10}^{"}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=10\text{'}\text{'}\times \sin 0^{\circ }{20}^{\text{'}}\\ h=10\text{'}\text{'}\times \sin {0.333}^{\circ }\\ \Rightarrow h=0.0582\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks is $0.0582\text{'}\text{'}$

To determine

(c)

Find the height of gage blocks required to set the angle $2^{\circ }{26}^{\text{'}}$ on a ${10}^{"}$ sine plate.

Answer to Problem 8A

Height of the gage blocks $=0.4245\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a 10" sine plate is $2^{\circ }{26}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle $2^{\circ }{26}^{\text{'}}$ on a ${10}^{"}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=10\text{'}\text{'}\times \sin 2^{\circ }{26}^{\text{'}}\\ h=10\text{'}\text{'}\times \sin {2.433}^{\circ }\\ \Rightarrow h=0.4245\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks is $0.4245\text{'}\text{'}$

To determine

(d)

Find the height of gage blocks required to set the angle ${19}^{\circ }{51}^{\text{'}}$ on a ${10}^{"}$ sine plate.

Answer to Problem 8A

Height of the gage blocks $=3.3956\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a 10" sine plate is ${19}^{\circ }{51}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${19}^{\circ }{51}^{\text{'}}$ on a ${10}^{"}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=10\text{'}\text{'}\times \sin {19}^{\circ }{51}^{\text{'}}\\ h=10\text{'}\text{'}\times \sin {19.85}^{\circ }\\ \Rightarrow h=3.3956\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks is $3.3956\text{'}\text{'}$

To determine

(e)

Find the height of gage blocks required to set the angle ${25}^{\circ }{31}^{\text{'}}$ on a ${10}^{"}$ sine plate.

Answer to Problem 8A

Height of the gage blocks $=4.307\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a 10" sine plate is ${25}^{\circ }{31}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${25}^{\circ }{31}^{\text{'}}$ on a ${10}^{"}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=10\text{'}\text{'}\times \sin {25}^{\circ }{31}^{\text{'}}\\ h=10\text{'}\text{'}\times \sin {25.516}^{\circ }\\ \Rightarrow h=4.307\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks is $4.307\text{'}\text{'}$