=l 8 - Banchory Academy

1 9. trigonometry 2 - Sine, Cosine Rule, Area of 'IriangleTwo yachts Ieave from harbour A sails on a bearing of 072ofbr 30 kilometres and B sails on a bearin-e of 140'for 50 kilometres and far apart are the two yachtswhen they have both stopped?Do not use a scale area of triangle is 38 square is 9 centimetres and BC is 14 the size of the acute anele ABCTwo boats leave port D sails on a course of057' Nat l3 miles per E sails on a bearing of 104"at l5 miles per 45 minutes Boat D receivesa distress call from Boat E requesting porttheir help as soon as far. to the nearest mile. would Boat D have to travel to reach Boat E?The area of the trianele shown is 36 cm'Show that sin triangle ABCAB = rl unitsAC = 5 unitsBC = 6 units\ that cos A383KU6.

2 A TV signal is sent from a a satellite S. to a village shown in the villa_se is 500 kilometres fiom signal is sent out at an angle of 35" 'rand is received in the village at an angle of 40'.Calculate the hei-eht of the satellite above the path in the diagramopposite runs parallelto the 'er leaves the pathat P, walks to the riverto bathe her feet at Rand rejoins the pathfurther on at the distance betweenthe river and the radio masts, Kangaroo (K), Wallaby (W)and Possum (P) are situatedin the Australian is 250 kilometres due south of Wallaby. 2-50kmWallaby is 410 kilometres fiom PossumPossum is on a bearing of 130" from the bearing of Possum from Wallaby. KDo not use a scale Each leg of a fblding table is preventedfrom opening too far by a metal metal bar rs 21 centimetres is fixed to the table top l4 centimetres fl'om thel2 centimetres fiom the :r aa.

3 :.,.:';. ",4. 4 :. :\1'/ -1'i ,,,i]; rir l. jii,',','rlir.,:t-i r ,L:hr l i'',' ,,.,'iti&'5RE5RE4RE3 KUa)b)Calculate the size of the obtuseangle which the table top makeswith the that the table legis 70 centimetres long,calculate the height of the and to the table legl-ringel*- ll cnr-3912 crn3RE10. A 'spaper group advertisesa new masazine on a heliurr-r the base of the balloon. B. trvo holding wiresare attached to the ground at A and distance from A to C is 130 A. the angle of elevation of B is 53'.From C, the angle of elevation of B is 68' ACalculate the height of point B above the not use a scale drawingI l. The bonnet of a car is held open. at an angle of 57', by a metal the diagram,PQ represents the bonnetPR represents the metal represents the distance fromthe base of the bonnet to the front of the is l0l centimetresQR is 98 centimetres aCalculate the length of the metal rod, not use a scale ABC has an area of 14 square is 6 centimetres and AC is 7 the possible sizes of angle BACAn orienteering course has 3 checkpoints -B is on a bearing of 030'and a distance of 8 km from is on a bearing of 155'fi'om Band a bearing of 105" from ) Explain clearly why ZABC = 5,5"b) Calculate the distance betweenpoints B and not use a scale B and -).

4 5RE4KU4RE2KU4RE805'40-53' 68"<_ t30m ----)98 cm14. Calculate the area of the , rescue boat. at R, picks up adistress call from a boat B. 3-50 kntaway, on a bearing of 120'.At the same time another distresscall comes from a yacht Y. which is170 km away from B and on a bearingof 220' from ) Prove that ZRBY = 80'b) The rescue boat is obliged to respond tothe nearest distress call the people on the boat or thoseon the yacht be rescued first ?(You must support your answer by showingworking).16. The diagram shows the positionof a helicopter base and two oil rigs,Delta and the helicopter base, the oil rig Deltais 35 kilometres away on a bearing of 050".From the same base, the oil rig Gammais 20 kilometres awav on a bearins of 125'.Calculate the distance between Delta and not use a scale.

5 The end wall of a bungalow is in the shape of arectangle and a triangle as shown in the roof has one edge inchned at an angle of 24"to the horizontal and the other edge inclinedat 42o Io the width of the house is the length of the longer sloping edge of the not use a scale 8. The diagram shows part of a golf distance AB is 420 distance AC is 500 metresand angle BAC = 52".Calculate the distance not use a scale +2KU4RE5RE4KU-413KU19. An aeroplane is f11'rng parallcl to the have been fined at A and Bas shown in the the aeroplane is flying at a certain beams from these lightsmeet exactly on the ground at angle of depression of the beam of light from A to C is 50".The angle of depression of the beam of light fiom B to C is 70'.

6 The distance AB is 20 the height of the aeroplane above sketch shows a plot of ground,PQRS, split into two the area of the plot of diagram shows the position of three airports, A, E andG is 200 kilometres fiom AE is 160 kilometres fiom AFrom G the bearing of A is 0-52' iFrom A the bearin-s of E is 216"How f'ar apart are airports G and E ?The side wall of a house. with measurementsas show n in the diagrarn. requires wall is in the shape of a rectangle and a average. a litre of paint will cover 8 square painter estimates that he will require l2 litres of this be enough pairrt?Justify your '6 m4RE13. A triangular i: shtrrr n inthe = 140 = 120 metresand angle PQR = 132'Calculate the length of not use a scale diagram shows two positions of a studentas she views the top of a position B.

7 The angle of elevation to T at thetop of the tower is 64oFrom position A. the angle of elevation to T at thetop of the tower is distance AB is metresand the height of the student to eye level is the height of the A field, ABC, is shown in the the area of the A ship, at position P. observes a lighthouse atposition Q on a bearing of 040'.The ship travels 30 krlometreson a bearing of 125'to position position R, the ship observesthe lighthouse on a bearing of 340".When the ship is at position R,how f'ar is it from the lighthouse?21. The diagram shows the positionsof an oilrig and two oilrig at R is 70 kilometresfrom a ship at A and 100 kilometresfiom a ship at B. Angle ARB = 65'.Calculate the distance not use a scale A trafflc island.

8 ABC. is shownin the the area of the tratflc island ifAB = metres. AC = l0 metresand angle BAC = 72"29. The diagram shows the goalpostson a rugby take a kick at goal, a player movesfrom T to position is perpendicular to TPA =40o and angle APB = l0'The distance AB between the goal postsis the distance from T to family wants to fenceoff a triangular part of their gardenfbr their pet have a long straight wall availableand two straight pieces of f'encing 6 metresand 7 metres in first erect the f'encing as shown in the ) Find the area of garden enclosed by the wall and the two pieces of f' ) What size should they rnake the angle at A so that the greatest area of gardenis enclosed'lGive a reason fbr your ship is first spotted at position R, which is on a bearing of 3l5' fiom alighthouse, L.

9 The distance between R and L is l0 kilometres. After the ship hastravelled due West to position T, its bearing f}om the lighthouse is 300". far has the ship travelled from R to T ' RE