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A right triangle  C^=A^+B^ I need to find B I know both C and A ,but not any angles Is...

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attomsriver | Student, Grade 9 | eNotes Newbie

Posted September 27, 2011 at 12:34 PM via web

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A right triangle  C^=A^+B^

I need to find B

I know both C and A ,but not any angles

Is it   Sqrt (C^ - A^)

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taylormath | High School Teacher | (Level 2) Adjunct Educator

Posted September 27, 2011 at 1:02 PM (Answer #1)

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I think you are on the right track to solving the missing side of a right triangle.  The Pythagorean Theorem states that:

`a^2+b^2=c^2` , where a and b are the legs and c is the hypotenuse.  The hypotenuse is the longest side opposite of the right angle. The legs form the right angle. Solve the Pythagorean Theorem for one of the legs, b:

`b=sqrt(c^2-a^2)` .  The + or - notation is missing since the side of a triangle is not negative. Here is an example problem.

Find leg b for a right triangle with a hypotenuse length of 20 and a leg length of 12.

`b=sqrt(20^2-12^2)`

`b=sqrt(400-144)`

`b=sqrt(256)=16`

The side length is 16.  The combination of three numbers that satisfy the Pythagorean Theorem are called Pythagorean triples.

12, 16 and 20 are a Pythagorean Triple.

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