Concept explainers
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
(1) ∠1
(2) ∠2
(3) ∠3
b. If
(1) ∠1
(2) ∠2
(3) ∠3
(a)
The values of angles
Answer to Problem 22A
The values of angles are
Explanation of Solution
Given information:
Given figure is
Calculation:
The angle which is formed at a point on outside a circle by two tangents, two secants or a secant and a tangent is equal to one half the difference of arcs intercepted by the tangents or secants.
Let us first calculate the value of arc AD,
The total angle subtended by the entire circular arc on the center is 360o.
Now,
Now, for calculating angle 2,
Similarly,
Now, for calculating angle 3,
Similarly,
Conclusion:
Thus, the values of angles are
(b)
The values of angles
Answer to Problem 22A
The values of angles are
Explanation of Solution
Given information:
Given figure is
Calculation:
The angle which is formed at a point on outside a circle by two tangents, two secants or a secant and a tangent is equal to one half the difference of arcs intercepted by the tangents or secants.
Let us first calculate the value of arc AB,
The total angle subtended by the entire circular arc on the center is 360o.
Now,
Now, for calculating angle 2,
Similarly,
Now, for calculating angle 3,
Similarly,
Conclusion:
Thus, the values of angles 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. If PS = 46, find (1)1 (2)2 b. If PS = 39, 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. a. If x = 24.93 mm and y = 28.95 mm, find Dia A. b. If x=78.36 mm y = 114.48 mm, find Dia A.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. If1 = 63, find (1) HK (2)HM b. If1 = 59.47, find (1) DC (1) HK (2)HMarrow_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 Dia A = 3.756" and Dia B = 1.622", find x. b. If x = 0.975" and Dia B = 1.026", find Dia A.arrow_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 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_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 3 = 47, find GH = 32, find (1) EF (2) 4 b. If 4 = 1753', find EF = 103, find (1) 3 (2) GHarrow_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. 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 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
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