Download Int 1 H`work Chapter 16.cwk (WP)

Chapter 16
Trigonometry
Exercise 16.1
1.
Make a sketch of the triangles shown below and mark on each triangle the hypotenuse,
the opposite and the adjacent sides to the angle.
a
b
c
x°
adj
x°
2.
Use the tangent (or tan) button on a scientific calculator to find the following
tangents (correct to two decimal places) :–
a
3.
x°
tan 40°
b
tan 44·5°
c
tan 89·8°.
A
Look at this right angled triangle with ∠ABC = 20°.
a
What is the length of the opposite side ?
b
What is the length of the adjacent side ?
c
Divide :- (opp ÷ adj) to get tan 20°.
d
Look up tan 20° on your calculator to check you get the same answer.
4 cm
20°
B
11 cm
C
Exercise 16.2
1.
Make a sketch of this right angled triangle.
A
COPY and complete to calculate the size of
the opposite side :–
=>
tan B
=
tan 34°
=
x cm
opp
adj
x
10
B
=>
x
=
10 x tan 34°
=>
x
=
..... cm (to 1 dec place)
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34°
10 cm
C
Trigonometry
2.
Use the method shown on the previous page to calculate the length of the opposite side
(x cm) of each triangle. (Give each answer to 1 decimal place.)
a
b
c
6 cm
65°
x cm
48°
10 cm
x cm
40°
x cm
11 cm
3.
hm
19°
Calculate the height of the tree.
21 m
4.
The angle of elevation of the top of a tree from
a point 21 metres from its foot is 19°.
A hill runs up from a main road to the house at the top.
The hill makes an angle of 12° to the road.
hill
Calculate how high the house is above the road.
12°
hm
road
35 m
Exercise 16.3
1.
Use the correct buttons on YOUR calculator to find the sizes of the angles A, B and C
(to the nearest degree) :a
2.
tan A = 1·376
b
tan B = 0·445
c
tan C = 0·052.
Make a sketch of this right angled triangle.
COPY and complete the following to calculate
the size of ∠PQR to 1 decimal place.
tan Q
=>
=>
=>
=
P
opp
12 cm
adj
tan x° = 12
10
Q
tan x° = .......
x°
10 cm
R
x = ... (to 1 dec. pl.)
∠PQR = .........
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Trigonometry
3.
Use the method shown on the previous page to calculate the size of the angle
marked in each triangle. (Give each answer to 1 decimal place.)
a
b
c
b°
12 cm
7 cm
15 cm
a°
c°
15 cm
4.
5 cm
8 cm
Ross is 180 centimetres tall. In the sunshine, he casts
a shadow on the ground 260 centimetres long.
Find the angle of elevation (x°) of the sun.
180 cm
x°
260 cm
5.
What is the angle of elevation of the top of a bell
tower 150 feet high, from a point on level ground
30 feet from the base of the tower ?
150 ft
x°
30 ft
Exercise 16.4
1.
Use the sine (or sin) button on your scientific calculator to calculate the following,
correct to two decimal places :–
a
2.
b
sin 60°
c
sin 81·5°.
Use the correct buttons on your calculator to find the sizes of the angles A, B and C
(to the nearest degree) :a
3.
sin 10°
sin A = 0·423
b
sin B =
1
c
8
sin C =
11
12
.
Use the sine ratio in these triangles to find the size of the opposite side in each case.
(Give each answer to 1 decimal place.)
a
b
c
20°
20 cm
x cm
65°
82°
18 cm
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27 cm
x cm
page 65
x cm
Trigonometry
4.
A kite is flying at an angle of 73° to the ground
and is attached to a taut string 100 metres long.
Calculate the height of the kite above the ground.
100 m
hm
73°
5.
A funicular railway is 275 metres long and the angle between the railway and the
ground is 14°.
275 m
hm
14°
Calculate the height (h metres) of the top of the railway above the ground.
6.
Use the sine ratio in these triangles to calculate the size of the angles asked for.
(Give each answer to 1 decimal place if necessary.)
a
b
c
a°
11 cm
22 cm
b°
A pencil 12 cm long lies with its end just resting
against the end of a book 7 cm thick.
12 cm
Calculate the angle between the table and
the pencil (x°).
8.
c°
7 cm
16 cm
7.
25 cm
14 cm
7 cm
x°
A plank is 2·5 metres long and is just touching the top of a wall, 1·61 metres in height.
2·5 m
1·61 m
x°
Calculate the angle between the plank and the ground.
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Trigonometry
Exercise 16.5
1.
Use the cosine (or cos) button on your scientific calculator to calculate the following,
correct to two decimal places :–
a
2.
b
cos 30°
c
cos 78°.
Use the correct buttons on your calculator to find the sizes of the angles A, B and C
(to the nearest degree) :a
3.
cos 12°
cos A = 0·788
b
cos B =
1
c
5
cos C =
7
8
.
Use the cosine ratio in these triangles to find the size of the adjacent side in each case.
(Give each answer to 1 decimal place.)
a
b
c
x cm
18 cm
24 cm
48°
x cm
19°
64°
15 cm
x cm
4.
Calculate the size of angle a, b and c in each of these triangles :(Give each answer to 1 decimal place.)
a
b
9 cm
5.
b°
8 cm
c°
12 cm
18 cm
a°
c
16 cm
22 cm
A telephone pole has a support cable 5·4 metres long
attached from its top to a point on the ground,
4·5 metres along from the base of the pole.
Calculate the angle the cable makes with the ground.
5·4 m
x°
4·5 m
6.
3·1 m
23°
x cm
The angle between the sloping roof on
this hut and the horizontal is 23°.
The sloping roof is 3·1 metres long.
Calculate the width of the hut.
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Trigonometry
O
A
O
S H C H T A
Exercise 16.6
1.
Use the correct ratio from SOHCAHTOA to find the value of x in each case.
(Give each answer to 1 decimal place.)
a
b
c
12 cm
x cm
x cm
14 cm
20°
d
x cm
72°
e
65°
9 cm
f
12 cm
7·5 cm
22 cm
11 cm
x°
22 cm
2.
16 cm
This picture shows a lamp-post 5·3 metres long, which
has toppled over and come to rest against the top of a
wall, 4·2 metres high.
5·3 m
4·2 m
x°
x°
Calculate the size of the angle (x °) between the
lamp-post and the ground.
x°
3.
wall
A plank, just touching the top of a wall, is 6·5 metres long.
Calculate how far away the foot of the plank
is from the wall.
6·5 m
30°
hm
4.
This flag is in the shape of a
right angled triangle.
50 cm
x°
Calculate the size of the
angled marked x in the flag.
20 cm
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Trigonometry
Revision Exercise
1.
Use your calculator to find the following (to two decimal places) :a
2.
b
cos 30°
sin a° = 0·866
b
tan 7°.
cos b° = 0·545
c
tan c° = 0·649.
Use the correct ratio from SOHCAHTOA to find the value of x in each case.
(Give each answer to 1 decimal place.)
a
b
x°
17 cm
18 cm
69°
x°
10 cm
d
x cm
9 cm
c
13 cm
x cm
e
20 cm
f
8·2 cm
x°
14°
4.
c
Use your calculator to find the sizes of the angles a, b, and c.
a
3.
sin 68°
Calculate the height of the tree.
hm
x cm 74°
19 cm
11 cm
4·2 m
25°
5.
A bus is parked next to a cable supporting
the bus park floodlights.
This cable makes an angle of 74° with the ground.
The cable is fixed at a point 2·5 metres from the
base of the pole.
74°
Calculate the height of the floodlight pole.
2·5 m
6.
The steps to the large slide are 5·2 metres long.
The bottom of the steps is 3·8 metres from a
metal support pole.
Calculate the size of the angle (x), between
the steps and the ground.
5·2 m
x°
3·8 m
©TeeJay Publishers 2007
page 69
Trigonometry