Concept explainers
(a)
Find the measure of arc JL.
(a)
Answer to Problem 53PPS
Explanation of Solution
Given :
In the graph , point M is located at the origin.
Calculation:
The length of the radius of the
Consider the point J . The right
So, in the right angled
We need to find the measure of arc JL.
Since the arc JL is minor arc , so its measure is equal to the measure of the related central angle.
So,
measure of arc JL =
So, measure of arc JL is
(b)
Find the measure of arc KL.
(b)
Answer to Problem 53PPS
Explanation of Solution
Given :
In the graph , point M is located at the origin.
Calculation:
The length of the radius of the circle is 13, since the x- coordinate of point L is 13 and radius is equal for each point on the circle.
Consider the point K . The right angle formed from drawing a perpendicular from K that intersects x -axis at A.
So, in the right angled triangle KMA , KM = 13 , MA = 12 , KA = 5.
We need to find the measure of arc KL.
Since the arc KL is minor arc , so its measure is equal to the measure of the related central angle.
So,
measure of arc KL =
So, measure of arc KL is
(c)
Find the measure of arc JK.
(c)
Answer to Problem 53PPS
Explanation of Solution
Given :
In the graph , point M is located at the origin.
Calculation:
From part (a) and (b) ,
Measure of arc JL =
Measure of arc KL =
By addition of arc Postulate,
So, measure of arc JK is
(d)
Find the length of arc JL.
(d)
Answer to Problem 53PPS
15.3 units.
Explanation of Solution
Given :
In the graph , point M is located at the origin.
Formula Used:
Arc length equation:
Calculation:
From part (a) ,
Measure of arc JL =
Radius of the circle is 13.
We need to find the length of arc JL = l
Use Arc length equation:
So, length of arc JL is about 15.3 units.
(e)
Find the length of arc JK.
(e)
Answer to Problem 53PPS
10.2 units.
Explanation of Solution
Given :
In the graph , point M is located at the origin.
Formula Used:
Arc length equation:
Calculation:
From part (c) ,
Measure of arc JK =
Radius of the circle is 13.
We need to find the length of arc JK = l
Use Arc length equation:
So, length of arc JK is about 10.2 units.
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