Find the exact area of the minor segment of a circle if radius is 10cm and the angle subtended is 5π/6

Question

amistre64 · Answer

t r^2/2

amistre64 · Answer

(5pi/6) 10(5) = 250pi/6

amistre64 · Answer

125pi/3 ?

anonymous · Answer

following so far, its converting the Sin(5π/6) into an exact ratio that gets me

amistre64 · Answer

so about 125 cm^2

amistre64 · Answer

dont need to convert sin; it just theta/2  r^2

amistre64 · Answer

the total area of a circle is 2pi/2  r^2  right?

anonymous · Answer

no this is a minor segment :/
need to use the A=(1/2)r^2(@-Sin@)
(where @ = theta and in radians)

amistre64 · Answer

define minor segment....is that new terminology?

amistre64 · Answer

aint it just the pie shaped piece?

anonymous · Answer

amistre64 · Answer

ohhhh minus the triangle lol

amistre64 · Answer

the triangle is side side/2 sin(t)

anonymous · Answer

Minor means small. :)

anonymous · Answer

yes but i need to use the above formula to figure out and converting the Sin part to exact ratios confuses the hell out of me

amistre64 · Answer

the sin(5pi/6) = 1/2

anonymous · Answer

really... how? :/

amistre64 · Answer

you take a 30 degree angle and look across it at the 1 and to the hyp of 2

amistre64 · Answer

basic trig angle

anonymous · Answer

but doesn't 5pi/6 = 150 degrees? :Z

amistre64 · Answer

yes; which has a reference angle of 30 degrees

amistre64 · Answer

150 and 30 have the same sin

anonymous · Answer

ah yes, I get you now! cheers for the help :)

amistre64 · Answer

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