1.62: Lengths and Angles in a Right Prism

Figure 3 shows a right prism $\displaystyle ABCDEF$. The cross section $\displaystyle BCF$ of the prism is a triangle.

The point $\displaystyle N$ lies on $\displaystyle BC$ such that $\displaystyle FN$ is perpendicular to $\displaystyle BC$.

(a) Show that $\displaystyle BN=5$ cm.

(b) Find, in cm to 3 significant figures, the length of $\displaystyle EN$.

The midpoint of $\displaystyle BF$ is $\displaystyle X$ and the midpoint of $\displaystyle FC$ is $\displaystyle Y$.

(c) Find, in degrees to one decimal place, the size of the angle between the plane $\displaystyle ABCD$ and the plane $\displaystyle AXYD$.

(d) Find, in degrees to one decimal place, the size of the angle $\displaystyle AYE$.