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- anonymous

Triangle ABC is a 45 degree-45 degree-90 degree in a sphere such that B is the center of the sphere and A and C are points on the sphere. Given the hypotenue of (trangle)ABC is 8√2 units, what is the surface area of the sphere?
A.) 320π square units
B.)85π square units
C.)256π square units
D.) 192π square units
The pic is there shown when you click on the question...Please help me

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- anonymous

- jamiebookeater

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- anonymous

- anonymous

okay, that image was not that helpful. What are the special properties on a 45-45-90 triangle?

- anonymous

i dont get what you asking

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- anonymous

What is special about having a triangle ABC that is a 45 degree-45 degree-90 degree?

- anonymous

It's a special triangle, correct?
http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri45.htm

- anonymous

yess

- anonymous

thats right

- anonymous

so we know the hypotenuse. Therefore we can figure out the radius (as it's the legs of the triangle). Then from the radius we know the sphere's surface area equation. Get it?

- anonymous

okay so i got D is that correct?

- anonymous

erm... I got something else.

- anonymous

what did you get... I am confused lol

- anonymous

Okay. You have the hypotenuse is 8Sqrt[2]
so the leg is simply 8.
Then we use the equation for surface area of a sphere (or derivative of the volume equation)

- anonymous

then we get 256pi or C

- anonymous

can you explain that?

- anonymous

Okay

- anonymous

\[Surface Area= 4\pi r^2\]
So we plug in r=8; 4*8^2= 4*64=256
We ignored the pi initially since we realized that the pi was already built into the answers. Then we get 256pi or answer C

- anonymous

ohhh thanks so much :)

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