Question

What is the side length of the largest square that can fit into a circle with a radius of 5 units?

use the Pythagorean theorem(a a squared plus b squared equals c squared) to solve this problem. (is it even possible to find the legs of the triangle when you only have the hypotenuse?)

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Answer 1

So 1st consider that it's a square! That's very important. So for a square, all 4 sides are equal.

And now considering that the given information is the diameter. So any angle made at the circle extended from the 2 points of diameter gives an angle of 90°

Now consider one triangle. So we already know that 2 sides of the triangle are equal (because they are 2 sides of a square) , has a side of 10 (diameter) and and angle of 90°. So remaining 2 angles are 45°

Now solve it by applying


`\sin(45) \: \: \: \: = x / 10 \\ (1 / √(2) ) = (x / 10) \\ 10 / √(2) \: = x`