Concept explainers
(a)
The value of angle E and angle F in the given figure.
Answer to Problem 27A
The angle E and angle F are equal to
Explanation of Solution
Given information:
The given value angle 1 is
The given value angle 2 is
Given figure is
Calculation:
The point P on the circle is the tangent point. Thus, the straight-line EF becomes tangent to the circle. The line joining center and the tangent point is perpendicular to the tangent. In other words, the angle EPO or the angle OPF is 90o.
In triangle OPE,
The value of angle E is
Now, let us calculate the value of angle F. The value of angle F can be calculated by considering triangle OPF.
Now, the angle
The value of angle F is
Now, the angle E and angle F are equal to
Conclusion:
Thus, the angle E and angle F are equal to
(b)
The value of angle E and angle F in the given figure.
Answer to Problem 27A
The angle E and angle F are equal to
Explanation of Solution
Given information:
The given value angle 1 is
The given value angle 2 is
Given figure is
Calculation:
The point P on the circle is the tangent point. Thus, the straight-line EF becomes tangent to the circle. The line joining center and the tangent point is perpendicular to the tangent. In other words, the angle EPO or the angle OPF is 90o.
In triangle OPE,
The value of angle E is
Now, let us calculate the value of angle F. The value of angle F can be calculated by considering triangle OPF.
Now, the angle
The value of angle F is
Now, the angle E and angle F are equal to
Conclusion:
Thus, the angle E and angle F are equal to
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Chapter 55 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. 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 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 1 = 6700' and 2 =9300', find: (1) AB (2) DE b.If 1 = 7500' and 2 =8500', find: (1) AB (2) DEarrow_forward
- Considering that the consecutive dials on the natural gas meter rotate in opposite directions, what is the current reading in cubic feet of usage? The initial direction is clockwise.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_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 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. 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 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 EF=84, find (1) EFD (2) HF (3) 1 b. If EF=79, find (1) EFD (2) HF (3) 1arrow_forwardDetermine 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 ST=2018 and SM=3807 find: (1) 1 (2) 2 b. If ST=2517 and SM=3524 find: (1) 1 (2) 2arrow_forward
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