Page 74 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

13. A surveyor stands 100 m from the base of a tower on which an aerial stands. He measures the angles of elevation to the top and bottom of the aerial as 56° and 49°. Calculate the height of the aerial.
15. From a coastal lookout point A, 100 m above 46 the sea, a sailor sights two boats B and C in the same direction. The angles of depression of the
two boats are 120°o and 26° respectively. Calcu- late the distance between the two boats.
16. A man standing on top of a cliff 90 m high is in 47 line with two buoys whose angles of depression are15°and2109o°.Calculatethedistancebetween
the buoys.
17. A woman of height 1.4 m standing on top of a building 34.6 m high views a tree some distance away. She observes that the angle of depression of the bottom of the tree is 35°, and the angle of depression of the top of the tree is 29°.
Assume that the building and the tree stand on level ground.
(a) Calculatethedistanceofthewomanfrom
the top of the tree measured along her line of
sight.
(b) Determine the height of the tree.
building across the square. He observes that the
(NW). Th
distance away, at an angle of depression of 53.5°. At what distance is the truck from the base of the building?
10. From a coastal lookout point P, 100 m above
angle of depression of the bottom of the building 18. A man of height 1.5 m standing on top of a
Fig. 11.8
41
the building is 25°. Both buildings stand on the
45
14. A surveyor stands 100 m from the base of a
tower on which aerial stands. He measures the angles of elevation to the top and bottom of the aerialas63°and578o°respectively.Determine the height of the aerial.
is 40° and the angle of depression of the top of building of height 48.5 m views another
Fig. 11.8
The posi is called angle me to the obj digits in east is 0 is 045°, S facts are i
43
sea-level, a sailor sights a boat at an angle of depression of 257o°. Calculate the horizontal distance of the boat from the sailor.
same level ground.
4121. A woman standing 20 m away from a tower observes the angles of elevation to the top and bottom of a flagstaff standing on the tower as 735°o and 70° respectively. Calculate the height of the flagstaff.
13. A surveyor stands 100 m from the base of a tower 44 on which an aerial stands. He measures the
angles of elevation to the top and bottom of the aerial as 56° and 498o°. Calculate the height of the aerial.
14. A surveyor stands 100 m from the base of a tower on which aerial stands. He measures the angles of elevation to the top and bottom of the aerial as 63° and 58° respectively. Determine the height of the aerial.
Bearings
The four cardinal directions are north, south, east and west. The directions mid-way between these directions are also used, that is, north-east (NE), south-east (SE), south-west (SW), and north-west (NW). These facts are illustrated in Fig. 11.88 below.
12. A surveyor stands 100 m from the base of a
tower on which an aerial stands. He measures the angles of elevation to the top and bottom of the aerial as 52° and 439° respectively. Deter- mine the height of the aerial.
68
W 458 458 E 458 458
(a) Calculate the distance of the man from the
596 Chapter 11 Trigonometry 1
base of the building across the square mea-
sured along his line of sight. Chapter11.indd(b5)96Calculate the height of the building.
NW
NE
N
SW
SE
15 From a coastal lookout point A 100 m above
8
t
t
9
9