Transcript Right Angled Triangles

Right Angled Triangles
The key points
Hypotenuse
• The longest side of a
right angled triangle
• Always opposite the
right angle
Hypotenuse
Pythagoras’ Theorem
C (hypotenuse)
A
B
• The two smaller sides,
squared and added
together equals the
hypotenuse squared.
• A2 + B2 = C2
• Only works for right
angled triangles
Find the length of ‘j’
15cm
hyp
12cm
j
• To find ‘j’, use P.T.
• Label the hypotenuse.
• 122 + j2 = 152
144 + j2 = 225
j2 = 81
j = 9 cm
Any other sort of questions?
Is this triangle right- angled?
Hyp?
6cm
4cm
5cm
• If it is then the
hypotenuse is 6cm
(longest side) and P.T.
will work.
• 42 + 52 = 16 + 25 = 41
62 = 36
so 42 + 52 = 62
P.T. does NOT work so
no right angle
So that’s it for right angled
triangles?
Unfortunately not
Don’t forget trigonometry.
(Worth big marks)
Key trigonometry facts
• Trigonometry links the size of the angles to
the length of the sides.
• Only works in right angled triangles.
• Can be used to find either a length or an
angle
• Don’t forget to check that your calculator is
working in degrees.
Help!
• Label the sides of your
triangle
• Hypotenuse (hyp) opposite the right
angle.
• Opposite (opp) opposite the angle you
know or want to find.
• Adjacent (adj) - the
remaining side.
0
25
hyp
adj
opp
Then pick your equation.
Sin 0 = opp
hyp
Cos 0 = adj
hyp
Tan 0 = opp
adj
0 is the Greek letter ‘theta’ which denotes an
angle.
But which one should I use?
• If you are trying to find an angle, work out
which two sides you know and use the
formula that contains them both.
• To find a missing side, work out which side
you want to find and the side you know and
then use the formula which contains both.
What?
Find the value of ‘f’
‘f ’
10cm
hyp
opp
300
adj
• We know the
hypotenuse and want
to find ‘f’ which is the
opposite.
• We use sin 300 = f / 10
10 x sin 300 = f
f = 5cm
Find the value of angle BCA
If I call angle BCA, ‘x’
A
tan x = 4 / 10 = 0.4
4cm
hyp
so x = tan-1 0.4
opp
B
10cm
adj
C
x = 21.8o ( to 1 d.p.)
How do I find an angle?
obtuse
reflex
acute
Find the value of 0
0
10cm
hyp
5cm
adj
opp
• Label the sides.
• We know ‘adj’ and
‘hyp’ so must use cos
• cos 0 = 5 / 10
cos 0 = 0.5
so 0 = 600 (cos-10.5)
One more for luck!
Find the value of ‘P’
Sin 400 = P / 5
5 Sin 400 = P
so P = 3.2cm (to 1 d.p.)
hyp
5cm
P cm
opp
400
adj
I hope this helped
I don’t want to have to
say
That’s all folks!
The end