Trigonometry / Pythagoras
A
1. ABCD is a rhombus whose diagonals are
24 cm and 40 cm.
Calculate the perimeter of this rhombus.
B
D 40 cm
C
24 cm
2. A telegraph pole is connected to the ground
by wires. Each wire is 8 metres long and is
fixed to the ground 4.5 metres from the pole.
h
8m
Use this information to calculate the height
of the telegraph pole.
4.5 m
3. The diagram opposite shows a ramp
outside a building.
The side view of the ramp is a
right angled triangle.
32 cm
0
Calculate, a , the angle made by the
ramp with the ground.
a0
1.66 m
4. Michael is looking at a hot air balloon in the sky.
From Michael’s position the angle of elevation
to the balloon is 350.
Calculate h, the height the balloon is above the
ground.
h
350
GROUND
75 m
2.7 km
5. Two runners leave from the same starting point
and head off in different directions.
Using the information in the diagram opposite,
Calculate how far apart the runners are.
42 0
3.5 km
60 m
6. Three trees are positioned as shown opposite.
A 75 0
38 0
Calculate the distance between trees A and C.
C
7. A flagpole 7 metres high is connected to
the ground by a metal wire. If the bottom
of the wire is 4.2 metres from the flagpole,
calculate the length of the wire.
7m
4.2 m
8. The side view of the roof of a house is
in the shape of an isosceles triangle, as
shown.
Calculate the length r of the sloping side
of the roof.
5m
r
14 m
d
9. The diagram shows the end view of a
symmetrical water trough.
50
0
40 cm
Calculate the distance d.
60 cm
B
10. A golfer is standing 120 metres from a
hole. He hits the bal,l which travels a
distance of 132 metres, and ends up
14 metres from the hole.
Calculate, x0, the angle by which the
golfer was off target.
120 m
x0
14
9.5mm
132 m
11. The diagram opposite shows the side view of a shed,
in the shape of a rectangle and a right angled triangle.
3.3 m
Calculate the width of the shed.
3.6 m
2.1 m
width
12. An aeroplane takes off at an angle of 180, as shown below.
850 m
h
180
Calculate the height, h, the aeroplane is above the ground after it has travelled 850 metres.
13. A flagpole 5 metres high is supported by a metal wire
which is connected to the ground, 3.2 metres from the
flagpole.
Calculate the size of the angle the wire makes with
the ground.
5m
3.2 m
B
14. The diagram oppsite shows triangle ABC with
measurements as shown.
Show that cos x = 15 .
Do not use a calculator.
5 cm
A
x
7 cm
6 cm
C
P
5 cm
15. The diagram opposite shows a triangle PQR.
Given that cos 600 = 12 , find the length of PR.
Q 60 0
Do not use a calculator.
8 cm
R
E
117 0
16. Calculate the area of the triangle
11.8 cm
14 cm
F
G
17. The diagram shows the position of an
airport and two aeroplanes flying at the
same height..
Calculate the distance between the
aeroplanes.
2200 m
3000 m
15
0
18. A piece of metal in the shape of a triangle has measurements as
shown.
(a) By calculating the largest angle in the triangle, determine
if the triangle is right angled.
(b) Calculate the area of metal in the triangle
7 cm
13 cm
15 cm
N
19. In the diagram opposite AB represents a main
road 28 kilometres long running due north.
AC and CB represent secondary roads.
Calculate the size of angle BAC.
B
23 km
28 km
65 0 C
A
20. The diagram shows a triangular shaped garden.
A jogger runs from one corner of the garden to
another, as shown..
1000
Calculate how far he has run.
50 0
65 m
A
21. A rhombus ABCD has diagonals of length
AC = 14 cm and BD = 22 cm.
D
Calculate the size of angle x.
B 14 cm
x
C
22 cm
22. The diagram opposite shows a tower with
a weather vane on top.
From a point A, the angle of elevation to the
top of the weather vane is 510.
From B, the angle of elevation to the top of
the weather vane is 670.
The distance from A to B is 25 metres.
h
Calculate the height, h, that the top of the
weather vane is from the ground.
A
23. Two identical industrial chimneys are
40 metres apart.
From a point A, the angle of elevation to
the top of one chimney is 700 and from
the same point the angle of elevation to
the top of the other is 600.
B
25m
40 m
h
Calculate the height, h, of the chimneys.
700
600
A