In each of the following figures, write down the adjacent side and opposite side of θ, and the hypotenuse of the triangle.
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1 [ In this eercise, all given values of cosine are rounded off to 4 significant figures. Give our answers correct to 3 significant figures if necessar. ]. In each of the following figures, write down the adjacent side and opposite side of, and the hpotenuse of the triangle. b a f c d e z 2. ind the value of cos in each of the following figures Given that cos 20 = , cos 40 = and cos 70 = , find in each of the following figures hung Tai ducational Press. ll rights reserved.
2 4. Given that cos 33 = , cos 52 = and cos 66 = , find in each of the following figures Given that cos 8 = 0.95, cos 36 = and cos 54 = , find in each of the following figures Given that cos 30 = , cos 50 = and cos 72 = , find in each of the following figures When moving from to along a slope in the figure, the horizontal distance covered is 30 m. If the angle between the slope and the horizontal is 2 and cos 2 = 0.978, find the distance between and on the slope m hung Tai ducational Press. ll rights reserved.
3 8. In the figure, is a rectangular lawn. and are two paths, where = 50 m and = 26. Lisa and Shirle walk to from and respectivel. Given that cos 26 = , how far (in m) does Lisa walk more than Shirle? 50 m 26 [ In this eercise, give our answers correct to 3 significant figures if necessar. ] 9. ind the value of each of the following cosine ratios. cos 5 cos 28 cos 39 (d) cos 60 (e) cos 72.8 (f) cos ind in each of the following. cos = 0.7 cos = 0.03 cos = (d) cos = 7 (e) 8 cos = (f) cos = 4. ind in each of the following figures (d) (e) (f) hung Tai ducational Press. ll rights reserved.
4 2. ind in each of the following figures (d) (e) (f) ind the value of each of the following. 2cos83 cos5 cos 50 cos 30 4 cos 7 5cos 33 2 (d) cos 78 6cos (e) cos ( ) (f) cos (4 5 ) 5 4. ind in each of the following. cos = cos cos = cos 45 cos cos = cos5 (d) cos = 4cos75 2cos83 (e) cos ( + ) = 0. 7 (f) cos 2 = The figure shows ΔPQR. Q 29 P 20 2 R Is ΔPQR a right-angled triangle? plain briefl. ind PQR hung Tai ducational Press. ll rights reserved.
5 6. In the figure, a wall stands verticall on the horizontal ground. ladder with the length of 3 m leans against the wall, where its foot is 0.8 m awa from the bottom of the wall. ind the angle between the ladder and the ground. 3 m 0.8 m 7. The figure shows a broken flag pole. ind the height of the original flag pole..5 m In the figure, is a kite. It is given that = 75 cm and = 65. ind the perimeter of. 9. In the figure, is a straight line ind. ind hung Tai ducational Press. ll rights reserved.
6 20. In the figure, is a straight line and =. ind the value of cos. cos 6 2. In the figure, and are right-angled triangles. ind. ind. 24 cm [ In this eercise, give our answers correct to 3 significant figures if necessar. ] 22. ind the value of sin in each of the following figures hung Tai ducational Press. ll rights reserved.
7 (d) (e) (f) ind in each of the following figures. L L M M L 25 3 N M 42 N N (d) M (e) L (f) L 30 N 2.5 L M N M N 24. ind in each of the following figures (d) (e) (f) hung Tai ducational Press. ll rights reserved.
8 25. In the figure, find the angle between the rope and the vertical line. 50 cm cm 26. In the figure, the four steps of a staircase are in equal height. wooden board leans on the staircase and makes an angle of 28 with the horizontal ground. Given that = 20 cm, find the height of each step of the staircase. 20 cm is a straight iron rod with the length of 80 cm. It is bent into the shape as shown in the figure. ind. 20 cm 50 cm 28. ind the value of each of the following. 3sin 82 sin 32 sin 60 sin 30 3 sin 8 8sin 4 (d) sin 72 sin 38 (e) sin ( ) (f) sin (3 5 ) hung Tai ducational Press. ll rights reserved.
9 29. ind in each of the following. (d) sin 60 sin = 2 sin 20 sin = (e) sin 50 3sin 40 sin = sin = sin 60 sin 4 6sin 20 sin 40 3sin 60 sin = (f) sin = 5 5sin ind the unknowns in each of the following figures is a straight line. 3. ind the unknowns in each of the following figures is a straight line is a straight line. 4 φ 27 is a straight line. 32. Wman is going to lean a ladder of 2.5 m high against a wall and fi a lamp on the wall at a position of 3.5 m above the ground. When his hands are up, the are 2. m above the ground (see igure I). In order to keep the ladder from falling, the angle between the ladder and the horizontal ground should be between 70 and 80, and Wman should stand onl at the middle of the ladder (see igure II). an Wman fi the lamp on the wall successfull? plain briefl. 2. m 2.5 m igure I igure II hung Tai ducational Press. ll rights reserved.
10 33. In the figure, is a trapezium. ind. cm 5 5 cm cm 34. In the figure, PQ is a building. and are two locations on the horizontal ground, where Q, and lie on a straight line. P = 0 m and P = 5 m. ind the distance between and. P 4 0 m 5 m Q [ In this eercise, give our answers correct to 3 significant figures if necessar. ] 35. ind the value of tan in each of the following figures L 8 9 M N (d) P 7 Q (e) T 65 U V (f) Z 55 X Y R hung Tai ducational Press. ll rights reserved.
11 36. ind in each of the following figures. L 4 M N (d) P R (e) T U V (f) Z X Q Y 37. ind in each of the following figures. 5 L 9 M N (d) P 4 (e) T 8 U (f) Y.3 X Q V R Z 38. ind the value of each of the following. 7 tan2 tan 2 tan 60 tan 30 3 tan 5 7 tan 3 2 (d) tan 80 4 tan5 (e) tan ( ) (f) tan (6 3) hung Tai ducational Press. ll rights reserved.
12 39. ind in each of the following. tan tan = tan = tan 80 tan = 4 tan 70 2 tan tan 30 4 (d) tan = tan7 tan 23 (e) tan = (f) tan = tan 50 tan 60 tan5 40. ind the area of the book cover as shown in the figure cm 4. In the figure, a rod with the length of 50 cm is perpendicular to the wall. The shadow of it on the wall is 40 cm long. ind the angle between the sunra and the wall. 50 cm 40 cm 42. ind the unknowns in each of the following figures is a straight line is a straight line hung Tai ducational Press. ll rights reserved.
13 43. ind the unknowns in each of the following figures is a straight line. 6 6 φ 4 is a straight line is a straight line. 44. In the figure, is a straight line, = 2. ind the area of Δ. 25 cm 45. In the figure, ric and esmond stand on two sides of a vertical monument T at locations and respectivel, and is a straight line. ind the distance between ric and the monument. ric T esmond m 46. The figure shows the penalt area in a football pitch. It is known that the two goalposts are 7.32 m apart and the penalt spot is located at m in front of the mid-point of the goalposts. ind the angle of shot for a penalt kick m m hung Tai ducational Press. ll rights reserved.
14 47. In igure I, is a trapezium. The pattern of a piece of cloth shown in igure II is composed of 32 trapeziums which are congruent to. an this piece of cloth cover a table top with the dimensions of 0 cm 80 cm completel? plain briefl. cm cm igure I igure II 48. The following are the lengths of the adjacent side and opposite side of an interior angle in each of the three right-angled triangles I, II and III: Triangle I: adjacent side = a +, opposite side = b Triangle II: adjacent side = a, opposite side = b Triangle III: adjacent side = a + 2, opposite side = b In which right-angled triangle is the value of tan the greatest? plain briefl. [ In this eercise, give our answers correct to 3 significant figures if necessar. ] 49. In each of the following figures, find the values of, cos, sin and tan hung Tai ducational Press. ll rights reserved.
15 50. ind and φ in each of the following triangles. φ 2 φ L M 5.2 φ 3 N 5. ind and in each of the following triangles M 52 L 9 N 52. ind the unknowns in each of the following figures is a straight line hung Tai ducational Press. ll rights reserved.
16 53. ind the unknowns in each of the following figures. 8 φ φ 40 is a straight line is a straight line. 54. In the figure, the length of the pendulum is m. When the pendulum makes an angle of 30 with the vertical line, how high does it rise? 30 m? 55. In the figure, is a straight line. 3 cm cm ind. ind. ind. (d) ind hung Tai ducational Press. ll rights reserved.
17 56. In the figure, is a sector. Its radius is cm and the angle at the centre is 70. is a point on such that. cm 70 ind the area of Δ. ind the area of the shaded region. 57. In the figure, and are straight lines ind. ind. Is parallel to? plain briefl. 58. igure I shows a piece of rectangular paper with the dimensions of 3 cm 5 cm. The paper is folded in a wa that the vertices of its two opposite angles coincide (see igure II). Let = cm. cm 5 cm 3 cm igure I igure II hung Tai ducational Press. ll rights reserved.
18 (i) press in terms of. (ii) Hence find the value of. Karl thinks that : = 3 : 5. o ou agree? plain briefl. 59. In the figure, is the rectangular container of the dump truck, where = 5 m and = 2 m. The container can rotate about point, where is the angle of the container made with the horizontal. is.6 m from the ground. 5 m 2 m.6 m ind. (Leave our answer in surd form.) ind. The dump truck is going to deliver some sand to a construction site with the maimum height limit of 6 m. When the truck unloads the sand, must be adjusted to 40. an the dump truck unload the sand in the construction site? plain briefl hung Tai ducational Press. ll rights reserved.
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