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Trigonometry

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

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)

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

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

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

Try these

15cm

w

x

53

72

8cm

49

z

12cm

y

65

12cm

Answers

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

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

Try these

F

7cm

25cm

15cm

8cm

G

5cm

9cm

10cm

6cm

H

I

Answers

- F 57.8
- G 73.7
- H 36.9
- I 29.1