What is the area under a chord with a central/arc angle of 125 and a radius of 8?

EDIT: I tried a few different methods and ended up with negative numbers. I really don't know what to do...

After reply 2:

EDIT: To clarify, I'm looking for are that is not a part of the traingle, but still part of the sector. Thank you Pavlov!

helperid1839321
Feb 13, 2018

#1**+1 **

The chord line and the the two radii of 8 form a triangle of which one angle is 125 degrees and the other two are

27.5 degrees (must add to 180 degrees)

Draw a line of length 'h' perpindicular to the chord which bisects the 125 degree angle .

Now you have two equal triangles with angles of 90 125/2 and 27.5 degree angles

Now use law of sines to find 'h'

sin 90 /8 = sin 27.5 /h = sin 62.5/(1/2chord)

h = 3.694 and chord = 14.192

Then area of the triangle = 1/2 b h where b is the chord

Area = 1/2 (14.192)(3.694) = 26.22 units^2

ElectricPavlov
Feb 13, 2018

#2**0 **

Sorry if I didn't clarify. I wasn't looking for the area of the triangle, I was looking for the area of the part of the section of the circle that wasn't a part of the triangle, but was ont the other side of the chord with the sector.

Thanks though!

helperid1839321
Feb 13, 2018

#3**+1 **

Then just find the area of the sector and subtract the area of the triangle

sector area = 125/360 x pi x 8^2 = 69.813 sq units

Now subtract the triangle for the area of the segment.....

ElectricPavlov
Feb 13, 2018