GCSE. 3D TRIGONOMETRY [ESTIMATED TIME: 70 minutes] (+ IGCSE) EXAM QUESTION PRACTICE 1. [4 marks] ABCDEFGH is a cuboid. Diagram NOT accurately drawn
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1 3 TRIGONOMETRY [ESTIMTE TIME: 70 minutes] EFGH is a cuboid. GSE (+ IGSE) EXM QUESTION PRTIE 1. [4 marks] 8 cm E F 5 cm H 17 cm G The cuboid has length 17 cm width 5 cm height 8 cm Work out the size of the angle that H makes with the plane EFGH. Give your answer correct to 1 decimal place.... Questions compiled
2 2. [6 marks] T 27 m 50 m is a horizontal rectangular field. = 50 m. = 27 m. T is a vertical mast. (a) The angle of elevation of T from is 19. alculate the length of T. Give your answer correct to 3 significant figures.... m (3) (b) alculate the distance from to T. Give your answer correct to 3 significant figures.... m (3)
3 3. [5 marks] The diagram shows a prism. M 12cm P L 20cm N 30 Q R Triangle PQR is a cross section of the prism. PR MP = 12cm ngle PRQ ngle PQR alculate the size of the angle that the line MR makes with the plane RQLN. Give your answer correct to 1 decimal place....
4 4. [5 marks] E H F 6 cm 8 cm 16 cm G The diagram shows a cuboid EFGH. = 8 cm, F = 6 cm and F = 16 cm. (a) Find the length of. Give your answer correct to 3 significant figures. =... cm (3) (b) Find the size of the angle between the line F and the plane GF. Give your answer correct to 1 decimal place.... (2)
5 5. [6 marks] The diagram shows a triangular prism EF = 8 cm F = 14 cm EF = 19 cm 8 cm E 14 cm 19 cm F (a) alculate the distance between and E. (b) alculate the angle between E and the plane EF.
6 6. [6 marks] + N h%#8(#$+e< #@@,(#5'./+2(#Q& 40 m "M+#/#&2+$+#('+=-%&5*+-&+L-(%k-&5#.+8(-,&2; $+%*+2,'+T'*5+-?+#;+ "+%*+2,'+3-,5L+-?+#+#&2+"#+_+YG+$; 0L'('+%*+#+P'(5%@#.+?.#8=-.'+#5+#; ^(-$+"M+5L'+#&8.'+-?+'.'P#5%-&+-?+5L'+5-=+-?+5L'+?.#8=-.'+%*+Hi; ^(-$+$M+5L'+#&8.'+-?+'.'P#5%-&+-?+5L'+5-=+-?+5L'+?.#8=-.'+%*+HXi; 9#.@,.#5'+5L'+2%*5#&@'+"$; `%P'+/-,(+#&*Q'(+@-(('@5+5-++*%8&%?%@#&5+?%8,('*; ;;;;;;;;;;;;;;;;;;;;;;;;;;;+$
7 7. [4 marks] The diagram shows a pyramid with a horizontal rectangular base PQRS. PQ = 16 cm. QR = 10 cm. M is the midpoint of the line PR. The vertex, T, is vertically above M. MT = 15cm. T S 15 cm R P M 16 cm Q 10 cm alculate the size of the angle between TP and the base PQRS. Give your answer correct to 1 decimal place....
8 8. [4 marks] V M 10 cm 10 cm The diagram shows a pyramid. The base,, is a horizontal square of side 10 cm. The vertex V, is vertically above the midpoint, M, of the base. VM = 12 cm. alculate the size of angle VM.... (Total 4 marks)
9 9. [4 marks] E is a square-based pyramid. E 12 cm 15 cm E = E = E = E = 12 cm = 15 cm alculate the size of angle E. Give your answer to the nearest degree....
10 10. [4 marks]
11 11. [5 marks] H G E F 3cm 5cm 7cm The diagram shows a cuboid EFGH. = 5cm = 7cm E = 3cm (a) alculate the length of G. Give your answer correct to 3 significant figures.... cm (3) (b) alculate the size of the angle between G and the plane. Give your answer correct to 1 decimal place.... (2)
12 12. [4 marks] V 12 cm 10 cm is the square base of the pyramid V. = = = = 10 cm. V = V = V = V = 12 cm. alculate the height of the pyramid. Give your answer correct to 3 significant figures.
13 13. [5 marks] pyramid has a horizontal square base with sides of length 230 metres. M is the midpoint of. The vertex, T, is vertically above M. The slant edges of the pyramid are of length 218 metres. alculate the height, MT, of the pyramid. Give your answer correct to 3 significant figures. T 218 m M 230 m 230 m... m
14 14. [5 marks] 12 cm E 9 cm F M 15 cm EF is a triangular prism. = 9 cm, = 15 cm and E = 12 cm. ngle = 90 M is the midpoint of. alculate the size of the angle between M and the plane F. Give your answer correct to 1 decimal place....
15 15. [6 marks] N T 10 m X 14 m, and are points on horizontal ground. is due North of and is 14 m. is due East of and is 25 m. 25 m vertical flagpole, TX, has its base at the point X on such that the angle X is a right angle. The height of the flagpole, TX, is 10 m. alculate the size of the angle of elevation of T from. Give your answer correct to 1 decimal place....
16 16. [4 marks] The diagram shows a cube EFGH. The sides of the cube are of length 5 cm. alculate the size of the angle between the diagonal H and the base EFGH. Give your answer correct to 1 decimal place. 5 cm F 5 cm G E 5 cm H...
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