Concept explainers
Solve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute.
a. If ∠ 1 = 67°00' and ∠ 2 =93°00', find:
(1)
(2)
b.If ∠ 1 = 75°00' and ∠ 2 =85°00', find:
(1)
(2)
(a)
The value of arc
Answer to Problem 26A
The values of arcs AB and DE are
Explanation of Solution
Given information:
The value of angle 1 is
The value of angle 2 is
The given figure is
Calculation:
The angles GHF and angle 1 are opposite angles. Thus,
Similarly, the angles EGM and angle FGH are opposite angles.
In triangle FGH, the angle GFH comes out to be
Now, an inscribed angle is one half the value of intercepted arc by the angle itself.
The line PMB is a straight line so,
Now, in triangle PMG, the sum of all angles should be equal to 180o.
Now, the value of arc DE can be found from the following formula,
The values of arcs AB and DE are
Conclusion:
Thus, the values of arcs AB and DE are
(b)
The value of arc
Answer to Problem 26A
The values of arcs AB and DE are
Explanation of Solution
Given information:
The value of angle 1 is
The value of angle 2 is
The given figure is
Calculation:
The angles GHF and angle 1 are opposite angles. Thus,
Similarly, the angles EGM and angle FGH are opposite angles.
In triangle FGH, the angle GFH comes out to be
Now, an inscribed angle is one half the value of intercepted arc by the angle itself.
The line PMB is a straight line so,
Now, in triangle PMG, the sum of all angles should be equal to 180o.
Now, the value of arc DE can be found from the following formula,
The values of arcs AB and DE are
Conclusion:
Thus, the values of arcs AB and DE are
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Chapter 56 Solutions
Mathematics For Machine Technology
- Solve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If1 = 63, find (1) HK (2)HM b. If1 = 59.47, find (1) DC (1) HK (2)HMarrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. Three holes are to be located on the layout shown. The 72.40-mm diameter and 30.80-mm diameter holes are tangent at point T, and TA is the common tangent line between the two holes. Determine (a) dimension C and (b) dimension D.arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If AB=116, find (1) 1 (2) 2 a. If AB=11256, find (1) 1 (2) 2arrow_forward
- Solve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If ST=2018 and SM=3807 find: (1) 1 (2) 2 b. If ST=2517 and SM=3524 find: (1) 1 (2) 2arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. Three posts are mounted on the fixture shown. Each post is tangent tothe arc made by the 0.650-inch radius. Determine (a) dimension A and(b) dimension B. Note: The fixture is symmetrical (identical) on each side of the horizontalcenterline ( CL ). All dimensions are in inches.arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If 3 = 47, find GH = 32, find (1) EF (2) 4 b. If 4 = 1753', find EF = 103, find (1) 3 (2) GHarrow_forward
- Solve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. All dimensions arein inches. a. If Dia A = 1.000", find x. If Dia A = 0.800",find x.arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If 1 = 25, find MPT= 95, find (1) KTP (2) PT (3) MP b. If 1 = 1730', find MPT= 103, find (1) KTP (2) PT (3) MParrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. Determine the length of x forGage A and Gage B. All dimensions are in inches. a. Gage A:y = 0.350", find x. b. Gage B:y = 0.410", find x.arrow_forward
- Solve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If EF=84, find (1) EFD (2) HF (3) 1 b. If EF=79, find (1) EFD (2) HF (3) 1arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. Points A, B, C, D, and E are tangent points. a. If AB=46.00 and DE=66.00 , find 1. b. If AB=53.00 and DE=70.00 , find 1.arrow_forwardSolve the following exercises based on Principles 11-14, although an exercise may require the application of two or more of any of the principles. Round the answers to 3 decimal places where necessary unless otherwise stated. a. If EF=160 mm, find HP . b If HP=160 mm, find EF . Round the answer to the nearest whole millimeter.arrow_forward
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