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?
The longest stick that will fit is from on corner to the opposite corner.
To calculate that diagonal, we use the pythagorean theorem:
s^2 = a^2 + b^2 + c^2
a, b, and c are 24, 18, and 12
s^2 = 24^2 + 18^2 + 12^2
s^2 = 1044
s = 6√29
I hope this helped,