Download Trigonometry - by Rod Cameron

Trigonometric ratios
Study Sheet
1. Which of the following statements about the 3-4-5 right
triangle below right is not true?
A
sin 37 =
3
5
B
tan 37 =
3
4
C
cos 37 =
3
5
D
cos 37 =
4
5
A
37
5 cm
4 cm
B
3 cm
C
2. Use the diagram and the trigonometric table to choose the
correct statement.
25
65
building
250 m
degrees
sine
Cosine
tangent
25
0.4226
0.9063
0.4663
65
0.9063
0.4226
2.1445
A
You can use tan 65 to establish the height of
the building
B
You can use sin 65 to establish the height of
the building
C
You can use the cos 25 to establish the
height of the building
D
Neither A, B or C is true
Trigonometric ratios
Study Help
The diagram below left shows the trigonometric ratios for
CAB on a 3-4-5 right triangle.
sin CAB =
opposite
3
= = 0.6
hypotenuse
5
cos CAB =
adjacent
4
= = 0.8
hypotenuse
5
sin CAB =
opposite
3
= = 0.75
adjacent
4
A
37
5 cm
4 cm
B
3 cm
C
Tigonometric ratios can be used to determine missing sides
of right angle triangles.
Trigonometric ratios are based on similar triangles. If you
know an angle other than the right angle, and the length of
one side, you have enough information to establish the
length of all sides.
Consider these triangles
1
h
2
40
40
h
50 cm
75 cm
In the case of triangle 1, there is enough information to
opposite
, or the length
adjacent
adjacent
. There is not
hypotenuse
establish the height using tan 40 =
the hypotenuse using cos 40 =
of
enough information to use sine as you do not know the value
of either the opposite side or the hypotenuse.
For triangle 2, you know the value of the opposite, and can
use tangent (
opposite
)
adjacent
to find the height, or sine (
opposite
hypotenuse
to find hypotenuse, but not cosine, as you do not know the
value of either the adjacent or the hypotenuse.
)