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# C2 Arcs/Sectors question watch

1. Hi

I'm stuck on this question (please see attachment) and I just can't seem to work it out! I had this wild idea of working out the angle at the top of the sector in the segment and going from there, but that didn't work! I can't link together the two pieces of info they give, the length of Ab and the height from Ab to P. Please help!
Attached Images

2. You see where the angle theta is marked, the right angle triangle formed there, until the side hits the line AB is R-10.
3. So Using Phythagoras : r2 = (r-10)^2 + 50^2 20r = 260 r = 130
4. To find the length of the sector:
Find the angle: sinx = 50/130 x = 0.395 radians
l=130 x X = = 51.3

Im not too sure about this so can someone tell me if its right?
5. a)'s easy. u can work out b) on your own.

Not sure if the image is attached correctly
Attached Images

6. (Original post by LondonBoy)
To find the length of the sector:
Find the angle: sinx = 50/130 x = 0.395 radians
l=130 x X = = 51.3

Im not too sure about this so can someone tell me if its right?
I used cosine rule for part b:
cos A = 130² + 120² - 50²/ 2(130)(120)
= 0.92309...
A = 0.39479..
θ = 0.39479 x 2 = 0.78958..

so l= 130 X 0.78958
= 102.6454
= 103 cm

Thanks for your help guys.

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