Pythagorean Theorem Word Problem

Question

Word problems involving the Pythagorean Theorem are struggling to me. I do not understand how to do the following problems:

 

Solve and simplify the radical if necessary.

 

Kelly just bought a high def TV that has a 55 inch diagonal screen. the TV is 28 inches tall. Will the TV fit in a cabinet that is 52 inches wide?

 

**My attempt**

28²+55²=c²

784+3025=c²

√3809=c

--I stopped after this step because I was confusing myself.--

 

 

The glass for a picture window is 8 feet wide. The door it must pass through is 3 feet wide. How tall must the door be for the glass to pass through the door?

 

 

**I attempted them both but the last one really confused me. I do not even understand how to set up the problem for it.**

Answer 1

So, the Pythagorean Theorem says that for any right triangle, a² + b² = c².  But in order to use it you need to be careful about what those letters mean.  For a right triangle there are 2 "legs" and a "hypotenuse".  The legs are the two shorter sides that meet at the right angle.  The hypotenuse is the longest side which is usually drawn at an angle so it looks slanted.  You can also think of it as being across from the right angle.  "a" and "b" are just the names for the legs, and it doesn't matter which one you call "a" and which one you call "b".  "c" has to be the hypotenuse though.

 

For the first one, just keep in mind that "c" is always the hypotenuse (diagonal / longest side) of the triangle.  So to solve it you just need to plug the 55 in for "c" instead of "b", and then try and solve for "b".  Lots of rectangle problems involving the diagonal will use the pythagorean theorem, and the diagonal will be "c" while the length and width (or width and height) of the rectangle are "a" and "b".

 

The idea for the second problem is similar.  If you're trying to fit a large object through a door, you will slant it so that it will fit diagonally, since that's the longest part of the doorway.  So if the object is 8 feet wide, that's your "c" value again.  The 3 foot width can be either "a" or "b", and then you solve it just like the first one.

 

If you need help actually solving the equations or simplifying radicals, let us know!