January 2022 MHF4U76 SUMMATIVE PAPER Z Page S of 8 Paper 2 Section B [Total Marks: 30] 5. [Maximum mark: 14] Two straight fences meet at point A in a garden. A sprinkler head is installed at point P. Water can reach a maximum distance of r metres. Point D is on one fence and point E is on the other, such that PD = PE = PA = r and DPE = 0 radians. This is shown in the following diagram. The length of the arc DE shown in the diagram is 3 m. (a) Write down an expression for r in terms of 8. [1] (b) Show that the area of the field that the water can reach is ;= (6 207 (0 + sin 0). [4] (c) The area of field that the water can reach is 6.29 m?. Find the value of 0. [2] (d) Hence, find the size of DAE [2] January 2022 MHF407b SUMMATIVE PAPER 2 Page 6 of 8 Question 5 continued.. diagram. A new fence is to be constructed between points B and C which will enclose the filed, as shown in the following 12 m Point C is due west of B and AC = 12 m. The bearing of B from A is 195. (e) (1) Find the size of ABC. (ii) Find the length of new fence required. [5]