Vertical Tower 1

MA represents a vertical tower. Points A, B, and C lie in the same horizontal plane. MB and MC are wire stays, each of length 20 meters. The angle of elevation of M at B is x&deg. ∠MCB is z&deg, and ∠ABC = y&deg = ∠ACB.

1. Prove that BC = 40 cos z.
2. Show that BC = 40(cos x)(cos y).
3. Calculate the magnitude of x if y = 42� and z = 71.8�.