CH22 Suppose each edge of the cube shown in the figure is 50

CH2.2

Suppose each edge of the cube shown in the figure is 5.00 inches long. Find the measure of the angle formed by diagonals CF and CH. Round your answer to the nearest tenth of a degree.

Solution

CF = (5^2+5^2+5^2) = (3(5)^2) = 53
CH = (5^2+5^2) = (2(5^2) = 52
FH = 5

sin(FCH) = FH/CF = 5/(53) = 1/3

FCH = arcsin (1 /3) = 35.26°

cos(FCH) = CH/CF = 52/(53) = 2/3

(FCH) = arccos (2/3) = 35.26°