cos/sine rule questions studies

Transcription

1 I Questionbank Mathematical Studies 3rd edition cos/sine rule questions studies 105 min 109 marks 1. On a map three schools, and are situated as shown in the diagram. Schools and are 625 metres apart. ngle ˆ = 102 and = 986 metres. 986 m 625 m 102 Find the distance between and. Find the size of angle Â.

2 2. In the diagram, triangle is isosceles. =, = 15 cm and angle is º 15 cm Find the size of angle ; the length of. (Total 4 marks) 3. The diagram shows the plan of a playground with dimensions as shown. 48 m 117º 57 m alculate the length ; the area of triangle. (Total 4 marks)

3 4. gardener pegs out a rope, 19 metres long, to form a triangular flower bed as shown in this diagram. 5 m 6 m alculate the size of the angle ; the area of the flower bed. (Total 5 marks) 5. In the diagram, D = 4 m, = 9 m, = 10 m, Dˆ = 90 and Dˆ = 100.

4 alculate the size of ˆ. alculate the length of. 6. The diagram shows a triangle in which = 17 cm. M is the midpoint of. Triangle M is equilateral. Write down (i) (ii) (iii) the length of M in cm; the size of angle M; the size of angle M. alculate the length of in cm.

5 7. The base of a prism is a regular hexagon. The centre of the hexagon is O and the length of O is 15 cm. Write down the size of angle O. Find the area of the triangle O. (1) The height of the prism is 20 cm. (c) Find the volume of the prism. 8. The diagram shows triangle in which angle  = 30, = 6.7 cm and = 13.4 cm. alculate the size of angle Ĉ. (4)

6 Nadia makes an accurate drawing of triangle. She measures angle  and finds it to be 29. alculate the percentage error in Nadia s measurement of angle Â. 9. farmer has a triangular field,, as shown in the diagram. = 35 m, = 80 m and  =105, and D is the midpoint of. Find the size of Ĉ. alculate the length of D. (5) The farmer wants to build a fence around D. (c) alculate the total length of the fence. (d) The farmer pays USD for the fence. Find the cost per metre. (e) alculate the area of the triangle D.

7 (f) layer of earth 3 cm thick is removed from D. Find the volume removed in cubic metres. (Total 18 marks) 10. In triangle, = 3.9 cm, = 4.8 cm and angle ˆ = cm cm alculate the length of. alculate the size of angle Ĉ. 11. Triangle is such that is 7 cm, angle ˆ is 65 and angle Ĉ is 30. (c) Sketch the triangle writing in the side length and angles. alculate the length of. Find the area of triangle. (1)

8 12. mir needs to construct an isosceles triangle whose area is 100 cm 2. The equal sides, and, are 20 cm long. ngle ˆ is acute. Show that the angle ˆ is 30. Find the length of. (Total 5 marks) 13. farmer wants to construct a new fence across a field. The plan is shown below. The new fence is indicated by a dotted line m 40 alculate the length of the fence. (5) The fence creates two sections of land. Find the area of the smaller section of land, given the additional information shown below m (Total 8 marks)

9 14. The following diagram shows a triangle. = 8 m, = 14 m, = 18 m, and  = º 8 m 14 m 18 m alculate the area of triangle ; the size of angle Ĉ. (Total 4 marks)

10 15. The diagram below shows a crane PQR that carries a flat box W. (PQ) is vertical, and the floor (PM) is horizontal. R 7.8 m 6.5 m Q 102º W 11.1 m h P M Given that PQ = 11.1m, QR = 7.8 m, PQˆ R =102 and RW = 6.5 m, calculate PR; angle PRˆ Q; (c) the height, h, of W above (PM). (Total 7 marks) 16. The diagram below shows a field D with a fence D crossing it. = 15 m, D = 20 m and angle ÂD = 110. = 22 m and angle Dˆ = D 22

11 alculate the length of D. alculate the size of angle ĈD. One student gave the answer to correct to 1 significant figure and used this answer to calculate the size of angle ĈD. (c) Write down the length of D correct to 1 significant figure. (1) (d) Find the size of angle ĈD that the student calculated, giving your answer correct to 1 decimal place. (e) Hence find the percentage error in his answer for angle ĈD. (Total 12 marks)