Allison:
If YV= 28 in, Find the length of arc VYX
Allison:
@dude
rishavraj:
Well you have the diamter, so you can the circumference right?? to get arc length you can use: \[(2~\pi~r)\times \frac{ \theta }{ 360 }\]
Allison:
Walk me through walk me throughhh
jimthompson5910:
Minor arc UV is 117 degrees The central angle that cuts off this arc is also 117 degrees This is shown in red The adjacent blue angle adds with the red angle to get 180 (red angle) + (blue angle ) = 180 117 + B = 180 where B is the measure of the blue angle What is the value of B?
Allison:
78
jimthompson5910:
You'll need to subtract 117 from both sides of 117 + B = 180
jimthompson5910:
B = 78 is not correct
Allison:
I got it, I think it's 19.05
jimthompson5910:
That's not correct. It appears you may have been calculating the length of the orange arc (as shown below). I've marked this measure as 78 degrees This is because the blue arc is B = 180-117 = 63, and this 63 degree angle is congruent to its vertical angle counterpart (angle VZW) which adds to 15 to get 78 So angle VZX = 78 degrees
jimthompson5910:
But instead you want the arc as shown below. Note how it goes through points V, Y and X
jimthompson5910:
We can say (green arc) + (orange arc) = 360 green arc = 360 - (orange arc) green arc = 360 - 78 green arc = 282 degrees Use this to determine the length of the green arc
Allison:
My God, my brain
Allison:
Okay give me a while
jimthompson5910:
Its a lot to remember, yeah
jimthompson5910:
alright
Allison:
I'm so lost ):
jimthompson5910:
Do you see how to get the blue angle?
Allison:
No
jimthompson5910:
The red and blue angles must add to 180, since they form a straight line (red angle)+(blue angle) = 180 117 + B = 180 B = 180-117 B = 63 The blue angle is 63 degrees Agreed or no?
Allison:
Yes
jimthompson5910:
Do you also agree that the blue and orange angles are the same measure?
Allison:
Yes
jimthompson5910:
So because the orange angle is 63 degrees, it adds to the 15 degree angle to get 63+15 = 78 This is the measure of arc VWX Check out the diagram below
Allison:
Okay
jimthompson5910:
Since we want to deal with arc VYX, this means we want to find the length of the pink arc in the diagram below The pink and green arcs form a full circle. This means the two measures add to 360
Allison:
282
jimthompson5910:
correct, that's the measure of the pink arc in degrees
jimthompson5910:
This means (282/360) of the full circle is covered by the pink arc. Multiply that fraction by the circumference to get your answer
Allison:
68.90
jimthompson5910:
I'm getting (282/360)*pi*28 = 68.9055988687361 which rounds to 68.91
Allison:
Thank you <3
jimthompson5910:
You're welcome
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