Determine the angle between the diagonal of a cube end the d

Determine the angle between the diagonal of a cube end the diagonal of its base, as shown in the figure. theta = degree An airplane flying at 550 miles per hour has a bearing of 51 degree. After flying for 2.5 hours, how far north and how far east will the plane have taveled from its point of departure? miles north miles east

Solution

The diagonal of a cube is given by side length *sqrt3

The diagonal of a face is given by side length *sqrt2

Using cosine law

a²=(a sqrt2)²+(a sqrt3)²-2(a sqrt2)(a sqrt3) cos theta

a²=5a²-2a²sqrt6   cos theta

4=2sqrt6 cos theta

cos theta=2/sqrt6

theta=cos^-1(2/sqrt6)

theta= 35.26 degree