In this lesson:
By the end of this lesson, you should be able to:
What is the longest straight rod that fits inside this 3-by-4-by-12 box?
The bottom face is a 3-by-4 rectangle: .
The base diagonal (5), the height (12), and the space diagonal form a right triangle.
The standing triangle has legs 5 and 12:
The longest rod is 13 ft.
The two steps combine into a single shortcut:
A room is 10 m by 8 m by 3 m:
Find the space diagonal of a box that is 2 by 3 by 6.
Use the formula or the two-step method. Try it before advancing.
A box's triangle was hidden but flat-based. A cone has no such face.
To find the right triangle, we have to slice the cone open.
The slant height is the hypotenuse; the radius and the height are the legs.
Slant height 15, radius 9:
A straw rests corner-to-corner in a cup. Which lengths are the legs?
A crate is 6 by 6 by 2 feet.
Find the longest rod that fits inside. Show both steps — no help.
Don't stop at step one — the base diagonal isn't the final answer In a cone, use the radius, not the diameter, as the leg
✓ Find one length, then use it as a leg of the next triangle ✓ A box uses two triangles; a cone uses a cross-section Don't stop at the intermediate length; mind radius versus diameter
Next: the theorem becomes distance on the coordinate plane.
Click to begin the narrated lesson
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles