A ladder 13m long rests against a vertical wall. Its foot is placed 5m away from the wall on level ground. Let θ be the angle that the ladder makes with the ground.
a. (a) Find, to the nearest metre, the height at which the ladder touches the wall.
b. (b) Calculate sinθ, cosθ and tanθ.
c. (c) Evaluate sin2θ+cos2θ and comment on the result.