The length one one leg of a right triangle is 6 inches. The hypotenuse measures 10 inches. What is the length of the other leg?

Question

what is the length of the other leg of the triangle

Answer 1

After you plot this on an x-y plot and find the distance, remember it.  You will find that three triangles appear an awful lot in algebra, geometry, and trigonometry because they have what I call "magic numbers"  -- values that make the math easy so the student can concentrate on the problem.
 
Here they are:
           angles             sides          
          45-45-90          n*1, n*1, n*SQRT(2)
          30-60-90          n*1, n"*SQRT(3), n*2
         (learn later)       n*3, n*4, n*5
Learn these three because you will see them often.

 

This problem describes a  6", 8", 10"  (that is, 3, 4, 5 with n=2) triangle

 

The Pythagorean Theorem  is C^2 = A^2 + B^2

   The problem gives:           10^2 = 6^2 + B^2

       so             B^2 = 10^2 - 6^2

                       B^2  = 64

                       B = 8        (or -8, which we ignore)