TOPIC 5 TRIGONOMETRY I REVIEW QUESTIONS FLUENCY The most urte mesure for the length of the third side in the tringle elow is: A 4.83 m B 23.3 m C 3.94 m D 2330 mm E 4826 mm 2 Wht is the vlue of x in this figure? A 5.4 B 7.5 C 0. D 0.3 E 4 3 Wht is the losest length of AG of the ue elow? A 0 B 30 C 20 D 4 E 7 John Wiley & Sons Austrli, Ltd
4 If sin 38 = 0.657, whih of the following will lso give this result? A sin 28 B sin 322 C sin 578 D sin 682 E sin 42 5 The ngle 8 52 34 is lso equl to: A 8. 5234 B 8 C 8. 86 D 8. 876 E 8. 786 52 34 6 Whih trigonometri rtio for the tringle shown elow is inorret? A sin α = B sin = C os = D tn = E tnθ = 7 Whih of the following sttements is orret? A sin 55 = os 55 B sin 45 = os 35 C os 5 = sin 85 D sin 30 = sin 60 E sin 42 = os 48 8 Whih of the following n e used to find the vlue of x in the digrm elow? A 28.7 sin 35 B 28.7 os 35 C 28.7 tn 35 D 28.7 sin 35 E 28.7 os 35 9 Whih of the following expressions n e used to find the vlue of in the tringle shown? 35 A 35 sin 75 B sin 75 75 C sin 35 35 D os 75 75 E os 35 0 If shool is 320 m S42 W from the polie sttion, wht is the true ering of the polie sttion from the shool? A 042 T B 048 T C 222 T D 228 T E 32 T John Wiley & Sons Austrli, Ltd
Clulte x, orret to 2 deiml ples. 2 Clulte the vlue of the pronumerl, orret to 2 deiml ples. 3 Clulte the height of this pyrmid. 4 A person stnding 23 m wy from tree oserves the top of the tree t n ngle of elevtion of 35. If the person s eye level is.5 m from the ground, wht is the height of the tree? 5 A mn with n eye level height of.8 m stnds t the window of tll uilding. He oserves his young dughter in the plyground elow. If the ngle of depression from the mn to the girl is 47 nd the floor on whih the mn stnds is 27 m ove the ground, how fr from the ottom of the uilding is the hild? 6 A plne flies 780 km in diretion of 85 T. How fr west hs it trvelled from the strting point? 7 A hiker trvels 3.2 km on ering of 250 T nd then.8 km on ering of 320 T. How fr west hs she trvelled from the strting point? 8 If 4 m ldder is pled ginst wll nd the foot of the ldder is 2.6 m from the wll, wht ngle (in degrees nd minutes) does the ldder mke with the wll? PROBLEM SOLVING The height of right squre-sed pyrmid is 3 m. If the ngle the fe mkes with the se is 67, find: the length of the edge of the squre se the length of the digonl of the se the ngle the slnted edge mkes with the se in degrees nd minutes. John Wiley & Sons Austrli, Ltd
2 A r is trvelling northwrds on n elevted expresswy 6 m ove ground t speed of 72 km/h. At noon nother r psses under the expresswy, t ground level, trvelling west, t speed of 90 km/h. How fr prt, in metres, re the two rs 40 seonds fter noon? At this time the first r stops, while the seond r keeps going. At wht time will they e 3.5 km prt? Write your nswer orret to the nerest tenth of seond. 3 Two towers fe eh other seprted y distne, d, of 20 metres. As seen from the top of the first tower, the ngle of depression of the seond tower s se is 59 nd tht of the top is 3. Wht is the height, in metres orret to 2 deiml ples, of eh of the towers? 4 A piee of flt pstry is ut in the shpe of right-ngled tringle. The longest side is 6 m nd the shortest is 2 m Find the length of the third side. Give your nswer in ext form. Find the sizes of the ngles in the tringle. 2 2 Prove tht the re of the tringle is equl to 4 2 m. 5 A yht is nhored off n islnd. It is 2.3 km from the yht lu nd 4.6 km from wether sttion. The three points form right ngled tringle t the yht lu. Clulte the ngle t the yht etween the yht lu nd the wether sttion. Clulte the distne etween the yht lu nd the wether sttion. The next dy the yht trvels diretly towrds the yht lu, ut is prevented from rehing the lu euse of dense fog. The wether sttion notifies the yht tht it is now 4.2 km from the sttion. Clulte the new ngle t the yht etween the yht lu nd the wether sttion. d Determine how fr the yht is now from the yht lu. John Wiley & Sons Austrli, Ltd
ANSWERS FLUENCY E 2 D 3 E 4 E 5 D 6 B 7 E 8 B 9 B 0 A x = 3. 06 m x = 83. 46 mm 2 9. 48 m 3 8. 25 mm 4 7. 6 m 5 26. 86 m 6 67. 98 km 7 4. 6 km 8 40 32 PROBLEM SOLVING. 04 m 5. 6m 59 2 280. 64 m 2:02:6.3 pm 3 33. 29 m, 2. 27 m 4 4 2 9., 5 70., 5 90. Are = se height 2 = 2 4 2 2 2 2 = 4 2 m. 5 60 3. 98 km 7.5 d. 33 km John Wiley & Sons Austrli, Ltd