Download TRIGONOMETRY REVISION

TRIGONOMETRY REVISION
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(2)
Question 3
Use your calculator to find, correct to four
decimal places:
(a) tan 62
Identify the sides and trigonometric ratio to
use
Question 1
(2)
(b) sin 1548
(a)
(2)
Question 4
(a) Convert 9.68 to degrees and minutes.
(b)
(b) Convert 2315 to decimal degrees.
Section A: Measurement, chance and data 5.5
(2)
Question 2
Which trigonometric ratio should be used to
find the value of the pronumeral in each of the
following diagrams?
(a)
(2)
Question 5
Find the value of the pronumeral in the
triangle below, where tan  = 4.
d
12
19.7 m
78

x
(b)

15 cm
12 cm
(2)
Find the value of the pronumeral in this
diagram.
Question 6
(1)
A kite is attached to a string 22 m long. If the
string makes an angle of 42.6° to the
horizontal, what is the height of the kite?
Question 9
26 cm
h
37
(2)
Find the equivalent first quadrant
trigonometric ratio for:
(a) sin115
Question 7
Question 10
(6)
A makeshift ramp is rested on a stack of
bricks as in the diagram.
0.6 m
(b) cos 330
r
h
18
(2)
Question 7
Find the value of the pronumeral in this
diagram.
1.4 m
If the ramp protrudes 0.6 m beyond the top of
the bricks:
(a) find the total length of the ramp
16.2 m
k
24
Question 8
(1)
Convert the conventional bearing S35E to
true bearing.
(b) find the height of the bricks
(c) find how far above the bricks the ramp
protrudes.
(2)
The angle of elevation of the top of a building
from a point on the ground 150 m away is
67. Calculate the height of the building
correct to the nearest metre.
Question 11
(6)
The diagram below shows two angles of
elevation (35° and 65°) of the top of a tower.
The points from which the angles are
measured are 20 m apart.
Question 14
h
65
b
35
20 m
(a) Write an equation involving the smaller
angle and h and b. Transpose it so that b is the
subject.
Section C: Measurement, chance and data 6.0
Question 12
(b) Write an equation involving the larger
angle and h and b. Transpose it so that b is the
subject.
(3)
The angle of depression from the top of a
120 m cliff to a boat out at sea is 2815. Find
the direct distance between the boat and the
top of the cliff, correct to two decimal places.
(c) Equate the two equations above to find the
height of the tower.
Question 13
(1)
Choose the correct answer.
The angle of elevation of the top of a tree
from a point on the ground 12 m away is 52.
What is the height of the tree is closest to:
(d) Find the horizontal distances from the
base of the tower, correct to the nearest metre.
Question 15
A cylindrical piece of hollow pipe is 35 cm
long and has both ends covered with
plastic. A tiny hole is made in the middle
of one end and a piece of wire is threaded
through. The wire does not bend. If the
pipe has a diameter of 15 cm, find:
(a) the angle the wire makes with the plastic if
it touches the opposite end where the plastic
meets the pipe
(b) the length of wire within the pipe.
35 cm
(c) What is the angle the wire makes with the
length of the cylinder.
Section D: Beyond 6.0
Question 16
A boat starts at A and sails 6 km on a bearing of
130° True to point B and then turns and sails on a
bearing of 200° True for another 10 km to C.
(a) How far south of A is C correct to the nearest
tenth of a kilometre? (draw the diagram first)
(b) What is the bearing, correct to the nearest
degree, of C from A in True Bearing?