Pythagorean theorem in 3D

The  exercise appears under the 8th grade (U.S.) Math Mission. This exercise practices the Pythagorean theorem in three dimensional objects.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the requested length: This problem has a three dimensional picture or drawing. The student is expected to use the Pythagorean theorem to find a requested length in the figure.Pti3d1.png

Strategies
Knowledge of the Pythagorean theorem in two dimensions and an ability visualize in three dimensions are encouraged to ensure success on this exercise.
 * 1) The Pythagorean theorem in three dimensions can be viewed as $$a^2+b^2+c^2=d^2$$. If the dimensions of a rectangular box are a,b and c, then d is the "long" diagonal of the box.
 * 2) The Pythagorean theorem in three dimensions is actually just the standard Pythagorean theorem performed twice.

Real-life Applications

 * 1) The long diagonal can be used to determine the largest objects that can fit inside a rectangular box.
 * 2) Problems of this nature are common on some standardized tests like the SAT and GRE.
 * 3) Many problems in this exercise are real-life applications.