s1s_ maths chapter 17c - graph (office 2007)

8/13/2019 S1S_ Maths Chapter 17c - Graph (Office 2007)

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3. The lid of a desk is 96cm long and 54cm wide. It slopes at 32 to thehorizon with its length horizontal. Find the inclination of its diagonal to thehorizon.


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4. A rectangular door ABCD, AB=2.40m and AD=1.20m, is free to rotateabout AB, which is vertical. If the door is opened through an angle of 44from the position ABCD to the position ABCD, find (a) the length CD and

(b) its inclination to the horizontal.


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7. A pyramid OABCD has a square base ABCD. O is vertically above thecentre of the square ABCD. If AB=8cm and OA=12cm, find(i) the height of the pyramid;(ii) the inclination of OA to the base ABCD;(iii) the angle between a sloping face and the base;(iv) the angle between adjacent sloping faces.


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8. The legs of a tripod are 1m long. The upper ends of the legs meet in apoint and the feet are at the vertices of an equilateral triangle of side 50cm.Find the height of the tripod and the inclination of a leg to the ground.


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9. The legs of a tripod OP, OQ, OR are 25cm in length, and they are openedso that P,Q,R are on a horizontal plane with PQ=PR=12cm and QR=9cm. Findthe height of the tripod and the inclinations of the legs to the horizon.


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10. A weight is supported by three chains attached to points in a ceiling atthe corners of an equilateral triangle of side 4m. The chains of lengths 6m,6m, 5m. Find the distance of the weight below the ceiling and theinclinations of the chains to the horizon.


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11. From a point A due north of a tower of height 100m, the elevation of topof the tower is 32 30. Find the elevation of the top of the tower from apoint B, 120m S 60 E of A.


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12. From the top of a cliff 100m high two buoys are observed in directions N32 W and N 25 W, their respective angles of depression being 3 12 and2 30. Find the distance between the buoys to the nearest ten metres.


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13. A and B are two points on a horizontal plane and C is a point 250mabove the plane. A is due south, and B is south-west of C; the angles ofdepression of A and B from C are 22 and 12 respectively. Find the distanceand bearing of A from B.


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14. A point B is due west of A and AB=80m. A tower which stands on thesame horizontal plane as A and B is due south of A. The angle of elevation oftop of the tower from A, B are 32 30 and 19 22 respectively. Find the

height of the tower.


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15. P, Q, R are three points on a horizontal plane, with QR=6000m and angleQPR = 110 20. From each of the points P, Q, R the angle of elevation of thesummit of a mountain is 45 , find the height of the mountain summit above

the plane.


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16. A tower AB is observed from two points P, Q in the same horizontalplane as B, the foot of the tower. The length PQ=375m, and the angles BPQ,BQP, APB are 58 , 44 30 26 34 respectively. Find the height of the tower tothe nearest metre.


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17. An observer sees an aeroplane bearing N34 W at an elevation of 22 ,and one minute later its bearing is N75 W and its elevation is 25 30.Assuming that the aeroplane is travelling at a uniform speed in a straight

line at a height of 5000m, find its speed and direction.


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18. At two points, the distance between which subtends an angle 32 28 atthe base of the flagstaff, the angles of elevation of its top are 34 24 and25 14 respectively. If the distance between the two points id 56.5m, find

the height of the flagstaff, assuming the two points and the foot of theflagstaff are in the same horizontal plane.


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19. At a point A the angle of elevation of the top of a hill, 1000m high, is12 30 and the bearing from A is N16 22E. At a point B on the samehorizontal plane as A, the elevation is 19 and the bearing is S43 12E. Find

the distance and bearing of B from A.


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20. A man in a balloon observes that the angle of depression of an object onthe ground bearing due north is 37 . The balloon drifts 5.28km due east andthe angle of depression is now found to be 23 34. Find the height of theballoon.


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21. A tower is observed from two stations A and B. It is due north of A andnorth-west of B. B is due east of A and distant 100m from it. The elevationof the tower as seen from A is the complement of elevation of the elevation

as seen from B. Find the height of the tower.


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22. A flagstaff, 20m high, stands at the centre of a plot of land in the shapeof an equilateral triangle. From the top of flagstaff each side of the plotsubtends and angle of 40 . Find the length of a side of the plot.


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23. From a point A on a level plane the angle of elevation of a kite is , thekite being due south of A. From a point B, which is a distance d m south ofA, the kite is seen northwards at an elevation . Find the height of the kite.

s1s_ maths chapter 17c - graph (office 2007)

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