Question 70763
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^2 = a^2+b^2}}} 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^2 = a^2 + b^2}}}:
{{{10^2 = 5^2 + b^2}}} Simplify and solve for b.
{{{100 = 25 + b^2}}} Subtract 25 from both sides of the equation.
{{{75 = b^2}}} Now take the square root of both sides.
{{{b = sqrt(75)}}} 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(75) = 5sqrt(3)}}}units