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# C2: Trig & radians watch

1. Hi everyone,

I've got a question that I find really hard. It comes with a diagram that I don't know how to reproduce here, but basically it's a sector of a circle, with a cord forming a triangle within the sector. The section of the sector that is not in the triangle is shaded grey.

The angle of the sector is The radius is 10cm.

Show that the area of the shaded segment is

My hunch was to have the area of the sector minus the area of the triangle, but calculating the area of the triangle using sin, not cos. It's the cos part that I'm struggling with. Can anyone give me any tips?

2. (Original post by marcsaccount)
Hi everyone,

I've got a question that I find really hard. It comes with a diagram that I don't know how to reproduce here, but basically it's a sector of a circle, with a cord forming a triangle within the sector. The section of the sector that is not in the triangle is shaded grey.

The angle of the sector is The radius is 10cm.

Show that the area of the shaded segment is

My hunch was to have the area of the sector minus the area of the triangle, but calculating the area of the triangle using sin, not cos. It's the cos part that I'm struggling with. Can anyone give me any tips?

3. (Original post by brianeverit)
Thanks Brianeverit! Does this apply to non-rightangled triangles too?
4. So I've got the right answer now using .

...although this exposes a problem in my understanding! I thought the above only applied to right angle triangles...I guess it's easy to see, obviously the right angle has to by so the one of the other angles is and the other angle therefore has to be but I really don't understand how this can hold for non-rightangled triangles when none of the angles are . Could anyone elucidate for me?

Braineverit - thanks for your help.
5. (Original post by marcsaccount)
So I've got the right answer now using .

...although this exposes a problem in my understanding! I thought the above only applied to right angle triangles...I guess it's easy to see, obviously the right angle has to by so the one of the other angles is and the other angle therefore has to be but I really don't understand how this can hold for non-rightangled triangles when none of the angles are . Could anyone elucidate for me?

Braineverit - thanks for your help.
It holds for ANY value of theta.
Attached Images
6. Notes for C1-C4.pdf (918.2 KB, 50 views)
7. Brianeverit, thanks once again

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