Trigonometry

1
Trigonometry
2
What is trigonometry?

• It only works for right angle triangles
• It is useful in building and surveying to work
  out the height of buildings
• It is used by aeroplanes and space shuttles
  landing to make sure they do not crash

3
How does it work?

• First you need to be able to label the parts of a
  triangle
• The easiest is the longest side, the hypotenuse
• Where is it?

Hypotenuse (it is always opposite the right angle)
4
Labelling the sides

• You need to identify which angle (not the right
  angle) we know
• There are two other sides
• The opposite is the side opposite the angle,
  where is it?
• The adjacent is the other side, beside it. Where
  is it?

Hypotenuse
Opposite
Adjacent
5
SOHCAHTOA

• These are the equations you need to use to work
  out the angle
• They are
• SO/H
• Sin Opposite/Hypotenuse
• C A/H
• Cosine Adjacent/ Hypotenuse
• TO/A
• Tan Opposite/ Adjacent

6
Working Out One Side

• If you want to find an unknown side you first
  have to work out which part of SOHCAHTOA you are
  going to use
• E.g.

We know the hypotenuse and we need to find the
opposite side (x) Which equation do we use? Sin
O/H Sin is a button on the calculator Sin72
X/10 0.95 x/10 9.5m x (this is smaller than
the hypotenuse)
10m
x
72
7
Try these
15cm
w
x
53
72
8cm
49
z
12cm
y
65
12cm
8
Answers

• X 14.3cm
• Y 5.1cm
• W 10.6cm
• Z 9.1cm

9
Finding An Angle

• To find an angle you divide the two sides you
  know and press shift sin/cos/tan
• E.g.

We want to find out what angle a is? Which
equation do we use? Cos A/H Cos a 5/10 Cos a
0.5 A 60
10cm
a
5cm
10
Try these
F
7cm
25cm
15cm
8cm
G
5cm
9cm
10cm
6cm
H
I
11
Answers

• F 57.8
• G 73.7
• H 36.9
• I 29.1