Transcript Trigonometry - tandrageemaths

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;
• S=O/H
• Sin = Opposite/Hypotenuse
• C= A/H
• Cosine = Adjacent/ Hypotenuse
• T=O/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?
10m
x
Sin = O/H
Sin is a button on the calculator
Sin72 = X/10
72°
0.95 = x/10
9.5m = x (this is smaller than the
hypotenuse)
Try these:
15cm
w
x
72°
53°
8cm
49°
12cm
y
65°
12cm
z
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?
10cm
Which equation do we
use?
Cos = A/H
a°
5cm
Cos a = 5/10
Cos a = 0.5
A = 60°
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°