Download Right-angled triangles - AshburtonCollegeMaths

2013 (Y10 Trigonometry)
Exercise A:
(a) Find the square root of:
(1) 16
(4) 100
c
5m
(2) 81
(3) 36
4m
(5) 49
(b) Without using a calculator, estimate the square root of the following
numbers to the nearest whole number:
(1) 17
(2) 80
(3) 34
(4) 104
(5) 45
(6) 26.35
(c) Find the square root of the following numbers rounding as indicated:
(a) 15 (2dp)
(b) 78 (3dp)
(c) 35.67 (2sf)
(d) 500 (2sf)
(e) 0.0004537 (3dp)
(f) 21 724.7 (3sf)
(d) Calculate the following:
2
(1) 3 + 4
2
2
(2) 13 – 5
2
(3)
2
8 + 15
2
Exercise B:
Find the length of the hypotenuse in each triangle below, using Pythagoras’
theorem. Round your answers sensibly.
2.7m
9c
m
c
5m
4m
a
b
3.6m
m
7c
12m
3m
41
d
2013 (Y10 Trigonometry)
a
6 .8
d
4.7mm
3m
b
4m
24cm
m
8c
cm
21
6cm
c
Exercise C:
Find the length of the shorter side in each of the triangles below, using
Pythagoras’ theorem. Round your answers sensibly.
mm
Exercise D:
Find the marked side in each triangle, using Pythagoras’ theorem.
Round your answers sensibly.
15km
b
19km
13cm
6cm
c
a
7cm
11cm
d
42
5.63cm
4.1
m
8.71cm
e
7.4m
10
.3m
2.6m
f
2013 (Y10 Trigonometry)
Exercise E:
For each of the following problems draw a diagram first. Each time you should
see a right-angled triangle so that you can use Pythagoras’ theorem. Round
your answers sensibly.
(a) John goes for a walk in the dessert. He walks 8km north and then heads
east for 6km. How far is he away from his starting point?
(b) A classroom is 7m across the front of the room and 8m from front to
back. How long is the diagonal of the room?
(c) A flagpole is 8m high. A guy-wire runs from the top of the flagpole to
the ground, and is attached to the ground 3m from the base of the
flagpole. How long is the guy-wire?
(d) A ladder that is 3.2m long is leaned up against a wall so that the base of
the ladder is 80cm from the wall. How high up the wall will the ladder
reach?
(e) A ramp is being made. The base of the ramp is 2.1m long and the height
is 0.5m high. How long is the sloping part of the ramp?
(f) A ladder is leaning against a wall. It reaches 2.7m up the wall, and the
base of the ladder is 0.6m from the wall. How long is the ladder?
Exercise F:
For the following triangles write down the fractions for sin, cos and tan
(eg. for (a) sin = 4 )
12cm
5
5m
(b)
13cm
4m
5m

(a)

15km
m

(c)
8m
m
(d)

25k
20km
10
3m
6m
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2013 (Y10 Trigonometry)
Exercise G:
Find the following to 2 decimal places:
(a) sin 37
(b) tan 59
(d) tan 27
(e) cos 21
(c) cos 12
(f) sin 87
Exercise H:
Find  for each of the following, giving you answer to 2 decimal places:
(a) sin  = 0.9
(b) cos  = 0.8
(c) tan  = 2.5
(d) cos  = 0.16
(e) tan  = 0.04
(f) sin  = 0.3
8cm
b
10cm
Exercise I:
Calculate the marked angle for each of these triangles:
15cm
a
3m
d
c
7m
5m
10cm
13m
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2013 (Y10 Trigonometry)
Exercise J:
In this exercise you should draw a diagram for each question first.
(a) A tent pole is 2m high. The rope running from the top of the pole to the
ground is 3m long. What angle does the rope make with the pole?
(b) A swimmer is swimming towards a cliff. The cliff is 100m high and is
600m from the swimmer. What is the angle of elevation needed for the
swimmer to look at the top of the cliff?
(c) A shooter is aiming at a clay pigeon. The clay pigeons are released
vertically from a point on the ground that is 120m from the shooter. If
the shooter wants to hit the clay pigeon when it is 60m above the
ground what should be the angle between the gun and the ground.
(d) Regulations state that the angle between a ladder and the ground must
be between 70 and 76. A 2m ladder is placed against a wall, and the
foot of the ladder is 0.7m from the wall. Is this ladder at a safe angle?
(e) The diagram below shows the cross section of a swimming pool. What
angle (marked ) does the sloping bottom make with the horizontal?
(Hint: You need to create a right-angled triangle.)
3m
60m

40m
20°
37°
45
b
a
8m
20m
Exercise K:
Calculate the lengths of the marked sides. (exercise continues on the next
page)
2013 (Y10 Trigonometry)
6.3m
c
57°
d
63°
e
4m
20°
300m
Exercise L:
(a) A ladder that is 2.4m long leans against a wall, at an
angle of 65 to the ground. Find the height that the
ladder reaches up the wall.
2·4m
65°
(b) A plane takes off from Christchurch
airport an angle of 8 and travels 80km.
How much height has the plane gained?
?
80km
8°
(c) A tree casts a shadow of 12m when the
sun rays make a angle of 37 with the
ground. Find the height of the tree.
(exercise continues on the next page)
46
37°
12m
2013 (Y10 Trigonometry)
(d) A ladder that is 2.7m long leans against a wall, at
an angle of 73 to the ground. How far is the base
of the ladder from the wall?
2·7m
73°
(e) Sam wants to find the height of a tree
and measures angle to the top of the tree
as 42 when she is 20m away from the
tree. Sam’s height is 1.5m. What is the
height of the tree?
42°
6m
1·5m
b
10cm
6m
13.4m
d
c
4m
6cm
a
10
m
Exercise M:
Find the marked side or angle in each of these triangles:
63°
120km
f
e
17.9m
m
3c
250km
.
15
63°
6cm
g
h
11.8m
cm
6.25
m
13.7
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2013 (Y10 Trigonometry)
Exercise N:
In this exercise you should draw a diagram
first.
(a) A rectangular swimming pool is 50m long
and 12m wide. How far is it from one
corner to the opposite corner i.e. how long
is the diagonal?
(b) A plane takes off from the Dunedin
airport. By the time it is overhead
Palmerston the plane is still climbing and
its altitude (height above the ground) is
8km. Palmerston is 50km from the
Dunedin airport. At what angle to the
horizontal is the plane climbing?
(c) Chris drives up Baldwin street in
Dunedin. It is the steepest
street in the world, with an angle
of 21 with the horizontal. The
road up Baldwin Street is 1.2km
long. How much altitude will Chris gain as he drives up Baldwin street?
(d) Colin and Alex are warming up for a rugby match. They
are standing at one of the corners of the rugby field,
which measures 100m by 50m. Colin runs around the
perimeter of the field, but Alex runs straight to the
opposite corner and straight back. How much further does
Colin run?
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