What is the length of an arc on a circle?

Question

Please see image link for reference:
http://img253.imageshack.us/img253/2733/mage10ym3.png

What is the distance from R to Q?

Answer 1

If you draw a line from the center(O) of the circle to R
Angle ROQ will measure 2t

The perimeter of the circle is pi*d =12*pi

The arc length will be 2t/(2*pi) *(12*pi)
12*t

Answer 2

2t/360 * 12π = πt/15 units

the angle labeled t is an inscribed angle, so the arc is 2t. The formula for arc length when the arc measure is x degrees is x/360 * circumference = x/360 * 2πr

Answer 3

RQ = 12sin(t)

whoops - that's the chord

you wanted the arc

okay - so you have angleRQP = 90-t and angle QRP = 90-t

2(90-t) + ROQ = 180

therefore ROQ = 2t

360 degrees gives you circumference = 2.pi.r
2.pi.r.2t/360 = arc length

r = 6
pi = approx 3.14159265...

Answer 4

Whoa, deja vu....

This follows directly from the answer to your other question.

PQ = 12 * cos(t)

QR = 12 * sin(t)

Note that PQ² + QR² = 12² (sin²(t) + cos²(t)) = 12², obeying the Pythagorean Theorem.

Answer 5

arc RQ is 2tº
the circumference is 2π*6=12π
RQ is 2tº/360º of the circle, so
RQ=(2t/360) *12π
RQ=πt/15
If I knew t, I could give you a numerical answer.