• Nov 9th 2009, 02:47 AM
juliak
This is a question I did about 4 times and kept getting a weird answer. I feel like I know where the mess up just because of the obscenely large number but I don't know what the mess up IS.

Okay here is it.

Two circles, each of radius 14 cm, are drawn with their centres 20 cm apart. Find the length of their common chord. Find also the area common to the two circles.

Okay I found the common chord which is 19.6 cm.

So to find the area common to the two circles, I first find that area of the sector and then I find the area of the triangle formed with the chord and subtract the latter from the former.

THIS IS WHERE I BELIEVE MY MESSUP IS.

To find the area of the sector, the formula is (1/2)(r^2)(theta)

So I gotta find theta.

I use the triangle formed by the chord to find theta. I divide that triangle into 2 so that it is a right angled triangle and so that I can use SOHCAHTOA.

sintheta=opp/hyp
sintheta=9.8/14
theta=inverse sin(9.8/14)

(9.8 is the chord length divided by 2)

I get 44.41. I multiply that by 2. and I have what I presume is the accurate angle. I insert this all into the equation.

(1/2)(14^2)(88.8)
= 8704.36

WHAAAAAT? Okay that has to be wrong but I don't know how/where?

Finding the area of the triangle formed by chord:
base * height / 2
= 19.6*10 / 2
= 98
Nice looking number - looks accurate.

The answer to this question is 108 cm^2.
• Nov 9th 2009, 02:58 AM
Gusbob
You need to use radians, not degrees for the angle. The area of sector 1/2rētheta only works with radians.
• Nov 9th 2009, 03:02 AM
juliak
oops sorry
• Nov 9th 2009, 03:10 AM
juliak
Oh. Um I converted 88.3 to radians by multiplying it by pi/180

I got 1.54

so .5*15^2*1.54 = 151.03

151.03 0- 98 (area of chord formed with triangle) = 53 cm^2

That's not right either :S