SOLUTION: In the diagram, the length of Arc AB is (3y-9)times pi. What is the value of y? The circle's center from a to b is 144 degrees and has a radius of 12. It is hard to

Algebra ->  Formulas -> SOLUTION: In the diagram, the length of Arc AB is (3y-9)times pi. What is the value of y? The circle's center from a to b is 144 degrees and has a radius of 12. It is hard to       Log On


   

Question 33486: In the diagram, the length of Arc AB is (3y-9)times pi. What is the value of y?
The circle's center from a to b is 144 degrees and has a radius of 12.

It is hard to explain a question when you cant draw a picture. sorry
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
The length of an arc, S is given by S=rA where r is the radius and A is the angle IN RADIANS:

So, we have 144 degrees. What is this in radians?

Start with one thing you NEED to learn:
360 degree = 2 pi radians
--> 1 degree = +%282%2Api%29%2F360+ radians
--> 144 degrees = +144%2A%28%282%2Api%29%2F360%29+ radians

You can simplify this out a bit if you wish here:
+144%2A%28%28pi%29%2F180%29+
+%284%2Api%29%2F5+

Right then, S=rA
--> +S+=+12%2A%284%2Api%29%2F5+
--> +S+=+%2848%2Api%29%2F5+

So, this is equivalent to +%283y-9%29%2Api+

so, +%2848%2Api%29%2F5+=+%283y-9%29%2Api+
+48%2F5+=+3y-9+
+48+=+5%283y-9%29+
+48+=+15y-45+
+93+=+15y+
--> y = 6.2


jon.