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