Please answer these questions with detailed steps and reasoning

3. [Maximum mark: 7] The following diagram shows a rightangled triangle, ABC. with AC = 10:11:. AB = Gem and BC = Beta. The points D and F lie on [AC]. [BD] ls perpendicularto [AC]. BEF Is the arc of a circle. centred at A. The region R is bounded by [BD], [DF] and are BEF. diagram not In coal- (3) Find BAG. [2] (b) Find the area of R. [5] 4. [Maximum mark: 7] A paint spot X lies on the outer rim of the wheel of a paddle-steamer. The wheel has radius 3 m and as it rotates at a constant rate, X is seen entering the water every 4 seconds. H is the distance of X above the bottom of the boat. At time t: 0 , X is at its highest point. a) Find a cosine model for H in the form of HO) = A cos B(t C) + D. [4] b) At what time does X rst enter the water. [3]