SOLUTION: In the length of the right angle,find the length of the side not given.Give an exact answer and approximation to three decimal places. a=15,b=15

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Question 503327: In the length of the right angle,find the length of the side not given.Give an exact answer and approximation to three decimal places. a=15,b=15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are 15 and 15 this means that a=15 and b=15


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


15%5E2%2B15%5E2=x%5E2 Plug in a=15, b=15, c=x


225%2B15%5E2=x%5E2 Square 15 to get 225.


225%2B225=x%5E2 Square 15 to get 225.


450=x%5E2 Combine like terms.


x%5E2=450 Rearrange the equation.


x=sqrt%28450%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=15%2Asqrt%282%29 Simplify the square root.


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Answer:


So the solution is x=15%2Asqrt%282%29 which approximates to x=21.213.