Missing side lengths

Question

How do I solve the missing lengths of a right triangle when it has an angle of 45 a hypotenuse of M and one leg that is n and another leg that is square root of 2.

Answer 1

Hi, Frances,

You may want to draw a picture and label the angles and sides of it.  Note that the sides of a special right triangle with one angle 45 means that the other angle is also 45 degrees, so the base angle is 90 degrees.  Remember that the angle degrees in a triangle sum up to 180 degrees.  If one leg is the square root of 2, the other has to be the same.

   |   hypotenuse=M

n |                                            The hypotenuse of a special right with 45 degree angles is x√2.

   |_____                                   Just change "x" for "n" and simplify.

      n=√2

I am going to let you finish this problem.  I hope that my example has helped.  Susan C.

Answer 2

You have a 45-45-90 triangle.  Since it's a right triangle, if one angle is 45 degrees, the other angle has to be 45 degrees (180-90-45=45).

 

Both legs of this triangle are equal, since the angles opposite those legs are both 45 degrees.  So both legs equal the square root of 2.

 

For a 45-45-90 triangle, the hypotenuse is the square root of 2 times the length of a leg.  So the hypotenuse equals 2 (square root of 2 times the square root of 2).  (The Pythagorean Theorem demonstrates this.)