Question

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Answer 1

Answer:

96

Step-by-step explanation:

IT IS CONVENTIONAL to let the letter s symbolize the length of an arc, which is called arc length. We say in geometry that an arc "subtends" an angle θ; literally, "stretches under."

Now the circumference of a circle is an arc length.  And the ratio of the circumference to the diameter is the basis of radian measure.  That ratio is the definition of π.

π   =   C

D .

Since D = 2r, then

π = C

2r

or,

C

r  =   2π .

arc lengthThat ratio -- 2π -- of the circumference of a circle to the radius, is called the radian measure of 1 revolution, which are four right angles at the center.  The circumference subtends those four right angles.

arc length

Radian measure of θ  =   s

r

Thus the radian measure is based on ratios -- numbers -- that are actually found in the circle.  The radian measure is a real number that indicates the ratio of a curved line to a straight, of an arc to the radius. For, the ratio of s to r does determine a unique central angle θ.