A rectangular box is 24 inches long, 18 inches wide and 12 inches high.

(a) Find the length of the longest (straight) stick that will fit into the box.

(b) What angle (in degrees) does that stick make with the base of the box?

bigguy1989 May 26, 2018

#1**+1 **

a) We can apply a "3D" version of the Pythagorean Theorem here :

The longest stick that will fit is given by:

√[ 24^2 + 18^2 + 12^2 ] = √1044 ≈ 32.31 in

b) We needt to find the diagonal distance across the bottom of the box to first answer this....we can apply the Pythagorean Theorem here :

This is given by : √ [ 24^2 + 18^2 ] = √900 = 30

We can find the angle that the stick makes with the bottom of the box by using the inverse tangent

arctan ( 12 / 30) = angle ≈ 21.8°

CPhill May 26, 2018