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 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 = 6700' and 2 =9300', find: (1) AB (2) DE b.If 1 = 7500' and 2 =8500', find: (1) AB (2) DEarrow_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 DC = 35, find AB. b. If AB = 127, find DC.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. 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_forward
- Determine the distance AB if CO = 19.8 mm.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 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 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_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. 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 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_forward
- Find the values of cot45,sec45, and csc45.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_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 PS = 46, find (1)1 (2)2 b. If PS = 39, find (1)1 (2)2arrow_forward
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