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Unformatted text preview: Assignment 2: Triangles Due : 24 th September Name: ____________________ 1. The area of the triangle shown below is 2.21 cm 2 . The length of the shortest side is x cm and the other two sides are 3 x cm and ( x + 3) cm. x 3 x x + 3 (a) Using the formula for the area of the triangle, write down an expression for sin in terms of x . (2) (b) Using the cosine rule, write down and simplify an expression for cos in terms of x. (2) (c) (i) Using your answers to parts (a) and (b), show that, 2 2 2 2 2 3 42 . 4 1 2 3 2 3  =  x x x x (1) (ii) Hence find (a) the possible values of x; (2) (b) the corresponding values of , in radians , using your answer to part (b) above. (3) (Total 10 marks) 2. In a triangle ABC, C B A = 30, AB = 6 cm and AC = 2 3 cm. Find the possible lengths of [BC]. Working: Answer: .................................................................. (Total 3 marks) 1 3. Let be the angle between the unit vectors a and b , where 0 &lt; &lt; . Express  a b  in terms of 2 1 sin . Working: Answer: .......................................................................... (Total 3 marks) 4. Triangle ABC has AB = 8 cm, BC = 6 cm and C A B = 20. Find the smallest possible area of ABC. Working: Answer : .......................................................................... (Total 6 marks) 2 5. In the triangle ABC, A = 30, BC = 3 and AB = 5. Find the two possible values of B . Working: Answer: ......................................................................... ......................................................................... (Total 6 marks) 6. A farmer owns a triangular field ABC. The side [AC] is 104 m, the side [AB] is 65 m and the angle between these two sides is 60. (a) Calculate the length of the third side of the field. (3) (b) Find the area of the field in the form p 3 , where p is an integer. (3) Let D be a point on [BC] such that [AD] bisects the 60 angle. The farmer divides the field into two parts by constructing a straight fence [AD] of length x metres. (c) (i) Show that the area of the smaller part is given by 4 65 x and find an expression for the area of the larger part. (ii) Hence, find the value of x in the form q 3 , where q is an integer. (8) (d) Prove that 8 5 DC BD = . (6) (Total 20 marks) 3 7. The triangle ABC has an obtuse angle at B, BC = 10.2, A = x and B = 2 x . (a) Find AC, in terms of cos x . (b) Given that the area of triangle ABC is 52.02 cos x , find angle C . Working: Answers: (a) (b) (Total 6 marks) 8. In triangle ABC, C B A = 31 , AC = 3 cm and BC = 5 cm. Calculate the possible lengths of the side [AB]....
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 Spring '10
 wilson
 Math, Angles

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