The rectangular box shown in the figure has dimensions 8 6

The rectangular box shown in the figure has dimensions 8\" × 6\" × 2\" (a = 8, b = 6, c = 2). Approximate the angle formed by a diagonal of the base and a diagonal of the 6\" × 2\" side. (Round your answer to two decimal places.)

Solution

Let = angle formed by a diagonal of the base and a diagonal of 6\'\' x 2\'\' side

Assuming base of rectangular box = 8\'\' x 6\'\'

Diagonal of 8\'\' x 6\'\' base = (8²+6²) = 10
Diagonal of 6\'\' x 2\'\' side = (6²+2²) = 40
Diagonal of 8\'\' x 2\'\' side (opposite ) = (8²+2²) = 68

(68)² = (10)² + (40)² 2 (10)(40) cos
68 = 140 4010 cos
4010 cos = 72
cos = 72/(4010)
= 55.3°