Expert: Paul Klarreich - 10/10/2007

Question
What is the hypotenuse of a 90 degree angle that is 12 feet by 12 feet?

Answer
Questioner:   Cindy
Category:  Advanced Math
Private:  No
 
Subject:  plane geometry
Question:  What is the hypotenuse of a 90 degree angle that is 12 feet by 12 feet?

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Hi, Cindy,

First rule of understanding math:  ALWAYS USE THE VOCABULARY CORRECTLY.  

Angles do not have hypotenuses; only RIGHT TRIANGLES DO.  By misusing the vocabulary, you write things, such as the question above, that don't mean anything.  

So the vocabulary is:

Right triangle:  A triangle containing a 90-degree angle.

Hypotenuse: The side of a right triangle opposite the 90-degree angle.

Leg: A side of a right triangle adjacent to the 90-degree angle.

Then you can ask this meaningful question:

What is the hypotenuse of a right triangle whose legs are each 12 feet?

Now we can answer it:

Call the sides a,b,c, where c is the hypotenuse.  Then a=12, b=12 and:

c^2 = a^2 + b^2

c^2 = 12^2 + 12^2

c^2 = 144 + 144

c^2 = 288

c = sqrt(288)

c = sqrt(144) sqrt(2)

c = 12 sqrt(2)