Trigonometry

1
15-Nov-09
Trigonometry
Use trigonometry to calculate an unknown side on
a right-angle triangle when you know an angle and
a side.
10 cm
?
350
900
B Grade Topic
2
Every angle has a sine (sin), cosine (cos) and
tangent (tan). You can obtain these from a
scientific calculator sin30 0.5
3
You will need to know the names of a right-angle
triangles sides.
h
hypotenuse
o
opposite
300
adjacent
a
4
You will need to know the rules for trigonometry
and these are often remembered by the saying,
soh cah toa This helps you to remember sine
opposite hypotenuse s o/h cosine
adjacent hypotenuse c a/h tangent
opposite adjacent t o/a The rules
show the relationship 2 6/3
5
v
v
s o/h c a/h t o/a 2 6/3
o
10 cm
h
x
v
?
v
x
300
900
a
Label the sides Write down the rules Tick what
you want Tick what you know Two ticks ? the
rule Use 2 6/3 to decide how to calculate
sin300 ?/10 0.5 ?/10 ? 0.5 x
10 ? 5 cm
6
x
v
s o/h c a/h t o/a 2 6/3
o
10 cm
h
v
v
v
x
300
900
a
?
Label the sides Write down the rules Tick what
you want Tick what you know Two ticks ? the
rule Use 2 6/3 to decide how to calculate
cos300 ?/10 0.8660 ?/10 ? 0.8660 x
10 ? 8.66 cm
7
v
v
s o/h c a/h t o/a 2 6/3
o
?
h
x
v
12 cm
x
v
300
900
a
Label the sides Write down the rules Tick what
you want Tick what you know Two ticks ? the
rule Use 2 6/3 to decide how to calculate
sin300 12/? 0.5 12/? ? 12
0.5 ? 24 cm
8
10 cm
1.
4.
?
?
8 cm
200
300

• 3.42
• 18.13
• 2.68
• 16
• 13.06
• 7.14

5.
20 cm
?
2.
250
400
10 cm
?
6.
3.
5 cm
?
350
150
?
10 cm