Question

PLEASE HELP!!!
The rectangular box shown in the figure has dimensions 10" 7" 3" (a = 10, b = 7, c = 3). Approximate the angle formed by a diagonal of the base and a diagonal of the 7" 3" side. (Give the answer to two decimal places.)

Answer 1

[Not sure about this since im learning the same thing, could be all wrong.]
For a-b diagonal length
\[x^2 = 10^2+7^2 = 149\]\[x = \sqrt{149} = 12,2\] and for b-c diagonal
\[y^2 = 7^2 + 3^2 = 58\]\[y = \sqrt{58} = 7,616\] and a-c
\[z^2 = 12,2^2 + 7,616^2 = 206,84\]\[z = \sqrt{206,84} = 14,38\] so angle would be
\[\cos \theta = 7,616\div14,38\]\[\theta = 58,01\]

Answer 2

It's 58.19, thnx though