SOLUTION: Hello, I need help with this: If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg? Thank you

Algebra ->  Triangles -> SOLUTION: Hello, I need help with this: If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg? Thank you      Log On


   

Question 70763: Hello,
I need help with this: If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg?
Thank you
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Are you familiar with the "Pythagorean theorem"?
This is the theorem that shows the relationship among the three sides of a right triangle. In algebra, it looks like this:
c%5E2+=+a%5E2%2Bb%5E2 where:
c is the length of the hypotenuse.
a and b are the lengths of the two legs.
So, if you are given the lengths of any two sides of a right triangle, you can find the length of the third side using the Pythagorean theorem.
Let's apply this to your problem.
The hypotenuse is given as 10 units, so c = 10
One leg is given as 5 units, so a = 5
Now substitute these values of c and a into the formula c%5E2+=+a%5E2+%2B+b%5E2:
10%5E2+=+5%5E2+%2B+b%5E2 Simplify and solve for b.
100+=+25+%2B+b%5E2 Subtract 25 from both sides of the equation.
75+=+b%5E2 Now take the square root of both sides.
b+=+sqrt%2875%29 You really get two values when you take the square root of a number, a positive and a negative. But, because we are finding the length of a side of the triangle and length is a positive quantity, we can ignore the negative value.
The length of the other leg is:
sqrt%2875%29+=+5sqrt%283%29units