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Lethal
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Geometry question w/ a Circle. find area of a shaded region. (Harder problem)
 2 years ago
 2 years ago
Lethal Group Title
Geometry question w/ a Circle. find area of a shaded region. (Harder problem)
 2 years ago
 2 years ago

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Lethal Group TitleBest ResponseYou've already chosen the best response.0
dw:1345779977023:dw
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
I think what you have to do is to bisect the triangle into 60 degree up top and then the bottom left and right are still 30 degrees. then you do the 30 60 90 triangle thing.
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
i am stuck from there
 2 years ago

alexwee123 Group TitleBest ResponseYou've already chosen the best response.1
i did it a different way...
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
well explain.
 2 years ago

alexwee123 Group TitleBest ResponseYou've already chosen the best response.1
with integrals...
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
well. it shouldn't be that complicated im only doing geometry.
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Area of minor segment \[A = \frac{1}{2} r^2 \left(\theta\sin\theta\right) \] But the only problem is \(r\) is not given..
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.0
I think I meant to post the area of a sector of a circle
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
you guys are thinking too hard its only like subtracting a sector
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Area of sector  area of triangle
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
But \(r\) is not given!!! Im thinking of using the cosine rule and sine rule to find \(r\) would it work?
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
here ill take it a bit further. dw:1345780578744:dw does that help?
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.0
It will not be hard to find \(r\)
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.0
Is the vertex of angle 120 is the center of the circle?
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
dw:1345780720301:dw looks like you can use the sine rule..
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.0
Okay, so yeah just do Area of Sector  Area of Triangle like what @Mimi_x3 suggested
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
soo all we need is the area of the circle and then we can use the 120/360 * pi r2 or something and subtract the area from that.
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
lets find \(r\) first
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
dw:1345780842471:dw
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
I got 8 as well using the sine rule
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Now its easy..you can do it yourself
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
ok so 64 pi is the area of the circle
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
and the area of the triangle left side is 1/2 * 4sqroot3 * 4
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
*2 to make up for the other side.
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
I will just use this formula\[A = \frac{1}{2} r^2 \left(\theta\sin\theta\right) \] No need to derive it
 2 years ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
and it must be in radians..so convert it..
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
oh heck nah jose
 2 years ago

alexwee123 Group TitleBest ResponseYou've already chosen the best response.1
you guys are thinking too hard o.0
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
oh wait i got the answer. just do 120/360 which is 1/3 and then i did 1/3 * 64pi which is the area of the circle and it is 64pi/3 and now subtract it by the area of the triangle which is
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
1/2 4sqrt3 * 4 or 8sqrt3 * 2 for the other side
 2 years ago

alexwee123 Group TitleBest ResponseYou've already chosen the best response.1
dw:1345781211630:dw dw:1345781273195:dw
 2 years ago

alexwee123 Group TitleBest ResponseYou've already chosen the best response.1
dw:1345781325118:dw
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
so the final answer is \[64\pi/3  16\sqrt{3}\]
 2 years ago

alexwee123 Group TitleBest ResponseYou've already chosen the best response.1
yes good job @Lethal
 2 years ago

Lethal Group TitleBest ResponseYou've already chosen the best response.0
yep, i would best response both of u but i can only do one. thx alex.
 2 years ago
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