Question 214697
A 45 - 45 - 90  triangle has a hypotenuse of length 15 units. What is the length of one of the legs? If necessary, round your answer to two decimal places.


Step 1.  Let c=15  be the hypotenuse.


Step 2.  Since the complementary angles are equal, their opposite sides are equal.  Let s be the side of the legs.


Step 3.  Using the Pythagorean Theorem given as the square of the legs (given as a and b) equal to square of the hypotenuse  or {{{c^2=a^2+b^2}}}.  For this example, a=b=s.


Step 4.  Then


{{{c^2=s^2+s^2}}}


{{{c=2s^2}}}


{{{c/2=s^2}}}


{{{sqrt(c/2)=sqrt(s^2)}}}


{{{sqrt(15/2)=s}}}


{{{s=sqrt(15/2)=2.739=2.74}}}


Step 5.   ANSWER:  The length of the both legs is 2.74 units.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J