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Trigonometry

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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 ... – PowerPoint PPT presentation

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Title: 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
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