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;
S=O/H
Sin = Opposite/Hypotenuse
C= A/H
Cosine = Adjacent/ Hypotenuse
T=O/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°