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Trigonometry
Objectives of this slideshow
•Identify opposite, hypotenuse and adjacent sides
• Define SOCAHTOA
•Apply SOCAHTOA depending on which rule we need
•Use all of the above to help find missing angles in a
right angled triangle
•Calculate missing sides of a right angled triangle
given another angle and length of one side.
Hypotenuse
opposite
adjacent
Label the opposite,
adjacent and
B hypotenuse
C
A
Top tips always find:
•Hypotenuse first as this is the easiest (always
opposite the right angle)
•Opposite second as it is always opposite the angle
we are interested in
•Finally the adjacent (which means next to) this one
is the only one left and is next to the angle but is
not the hypotenuse
A = adjacent
B = opposite
C = hypotenuse
Does
theopposite,
angle
Label the
adjacent,
and
we
are looking
at
hypotenuse
here.
make
a difference
toIf you
thehave
names
any of
B the
questions
write them
sides?
C
on your whiteboard
A
A = adjacent
B = opposite
C = hypotenuse
YES IT DOES!!!!
A = opposite
B = adjacent
C = hypotenuse
You need to remember this
Sine =
opposite
hypotenuse
Cosine =
adjacent
hypotenuse
Tangent =
opposite
adjacent
You should be able to tell what the size
of this angle is using your knowledge of
triangles.
Step
We
are
label
going
theto
sides
proveH,this
O and A (this order)
The1:
two
sides
are
using
trigonometry.
The
equal
length
so
it
Step 2: work out which
reason
picked an angle
must beI have
an isosceles
trigonometric
function we
that
we already
know is so
triangle.
It can’t
need
to use
basedbeonanthe info
that
we can be sure
we are
equilateral
we
are given.asInone
thisofcase we
getting
theiscorrect
answer
thegiven
angles
rightA
are
the Oa and
which
using
trigonometry which we
angle.
relates to tangent because
are unfamiliar with. Once we
Tangent = O/A
have
familiar with it
180° –become
90° = 90°
we can start looking at more
difficult
that we can 6cm
90° ÷ 2 =examples
45°
only solve using
trigonometry.
The
be 45°
Stepangle
3: themust
tangent
of this angle = 6/6 =1
to find the actual angle we do tan¯¹ (1) = 45°
6cm
Have a go at this question to see if you can find the yellow angle?
Click to the next
screen for a little
help
5cm
Step 1: label the
sides H, O and A
13cm
Step 2: which
function do you
use? SOHCAHTOA
Step 3: use the sine rule because sine = opp/hyp and these are the
two we know. Opp/hyp = 5/13
Sine¯¹ =
Tip if the answer you get seems like a wrong answer check through the steps that you have labelled the sides
correctly, used the correct function and if not you probably didn’t press the inverse function. You probably pressed
Sine and not Sine¯¹.
Cosine¯¹(13/9) = ____ why???
Don’t shout out your answer!!!
Because cosine is adjacent/hypotenuse and the
hypotenuse is always the biggest side. In this case
the adjacent side was bigger than the hypotenuse
therefore impossible to do.
3cm
Draw these triangles in your book (not to scale) and then work out the missing angle
Sine (O/H)
sine¯¹(3/4) = 48.6° (1dp)
Sine (O/H)
tangent (O/A)
tangent¯¹(6/5) = 50.2° (1dp)
sine¯¹(4/7) = 34.8° (1dp)
Find all the
missing angles
3cm
Draw these triangles in your book (not to scale) and then work out the missing angle
Sine (O/H)
sine¯¹(3/4) = 48.6° (1dp)
Sine (O/H)
tangent (O/A)
tangent¯¹(6/5) = 50.2° (1dp)
sine¯¹(4/7) = 34.8° (1dp)
Find the length of
the side labelled x
Step one what rule do we need to use?
Sine because we know the hypotenuse and we want to know the opposite
This time we can say that
We can multiply both sides
By 15 to get
sine(45 °) =
15 x sine(45 °) =
10.61cm(2dp) =
X
15cm
X
X
Find the length of
the side labelled x
Step one what rule do we need to use?
Cosine because we need to know the hypotenuse and we do know the adjacent
This time we can say that
We can multiply both sides
By X to get
Then we can divide both sides by
Cosine (45 °)
Cosine(45 °) = 8cm
X
X Cosine(45 °)
=
8cm
X = 8cm ÷ Cosine(45 °)
X = 11.31cm (2dp)
Draw these triangles in your book (not to scale) and then work out the missing angle
x
60°
45°
52°
36°
Show the angle
is 45° on any
right angled
isosceles
triangle using
trigonometry