Which of the following statements is true? A. The length of the hypotenuse of a

Question

Which of the following statements is true? A. The length of the hypotenuse of a special pi/4, pi/4, pi/2 right triangle is equal to twice the length of a leg opposite the pi/4 angle. B. The length of a leg of a special pi/4, pi/4, pi/2 right triangle is equal to half of the length of the hypotenuse. C. The length of the leg opposite either of the pi/4 angles of a special pi/4, pi/4, pi/2 right triangle with a hypotenuse of squareroot 2 is equal to 1. D. It is not possible for a special pi/4, pi/4, pi/2 right triangle to be isosceles.

Explanation / Answer

In a pi/4 , pi/4, pi/2 triangle, two angles are equal and the legs are equal to .

SO its an isosceles right triangle . And hypotenuse is leg length * sqrt 2 .

So if the legs are 1 unit each

Therefore according to pythagoras theorem

12+12=c2

c2=2

c=sqrt 2

Hence the correct option is C .

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