The angles of A and B are 45 degrees with C being 90 degrees. The distance from C to the hypotenuse (c) is 22″. I need the length of a and b of this triangle. Please include the formula that you used.

February 2nd, 2011 @12:53 pm

Ok so the line from angle C (90 degrees) to the centre of the hypotenuse? So that this creates an opposite right angle?

February 2nd, 2011 @1:12 pm

From the angles given, the triangle is a 45, 45, 90 right Triangle. The line from C to the hypotenuse bisects the triangle forming 2 congruent triangles to the original. That distance is 22 so to find the hypotenuse of 1 of those 2 triangles you’d use the Pythagorean theorem

22^2 + 22^2 = c^2

c = 31.11

That hypotenuse is also the legs of the original triangle so a and b also equal 31.11

February 2nd, 2011 @1:56 pm

by dropping an altitude to c measuring 22″, you get another triangle with 45,45,90

22″ is opposite a 45 angle, so the other side is 22″ opposite the 45 angle

(22)^2 + 22)^2 = sideA^2

484 + 484 = sideA^2

968 = sideA^2

31.1126 = side a

side b = side a = 31.1126

a^2 + b^2 = c^2

968 + 968 = c^2

1936 = c^2

44 = c

The line from C to the hypotenuse also forms a 45-45-90 right triangle. With this knowledge, the length of a & b are 22?2.

By the way, c = 22?2 * ?2 = 22 * 2 = 44.