Right Angled Triangles

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Right Angled Triangles

• The key points

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Hypotenuse

• The longest side of a right angled triangle
• Always opposite the right angle

Hypotenuse
3
Pythagoras Theorem

• The two smaller sides, squared and added together
  equals the hypotenuse squared.
• A2 B2 C2
• Only works for right angled triangles

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Find the length of j

• To find j, use P.T.
• Label the hypotenuse.
• 122 j2 152
• 144 j2 225
• j2 81
• j 9 cm

15cm
hyp
12cm
j
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Any other sort of questions?

• 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

Is this triangle right- angled?
Hyp?
6cm
4cm
5cm
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So thats it for right angled triangles?
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Unfortunately not

• Dont forget trigonometry.
• (Worth big marks)

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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
• Dont forget to check that your calculator is
  working in degrees.

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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.

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Then pick your equation.

• Sin ? opp Cos ? adj Tan ? opp
• hyp hyp
  adj
• ? is the Greek letter theta which denotes an
  angle.

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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.

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What?

• 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 f
10cm
f
hyp
opp
300
adj
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Find the value of angle BCA

• If I call angle BCA, x
• tan x 4 / 10 0.4
• so x tan-1 0.4
• x 21.8o ( to 1 d.p.)

A
4cm
hyp
opp
B
C
10cm
adj
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How do I find an angle?
obtuse
reflex
acute
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Find the value of x

• Label the sides.
• We know adj and hyp so must use cos
• cos x 5 / 10
• cos x 0.5
• so x 600 (cos-10.5)

x
10cm
5cm
hyp
adj
opp
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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
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I hope this helped

• I dont want to have to say

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Thats all folks!

• The end