Right Angled Triangles

1 / 18

# Right Angled Triangles - PowerPoint PPT Presentation

Right Angled Triangles. The key points. Hypotenuse. The longest side of a right angled triangle Always opposite the right angle. Hypotenuse. Pythagoras’ Theorem. The two smaller sides, squared and added together equals the hypotenuse squared. A 2 + B 2 = C 2

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Right Angled Triangles

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Right AngledTriangles

The key points

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

Hypotenuse

Pythagoras’ Theorem
• 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’
• To find ‘j’, use P.T.
• Label the hypotenuse.
• 122 + j2 = 152

144 + j2 = 225

j2 = 81

j = 9 cm

15cm

hyp

12cm

j

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

### 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.

Sin 0 = opp Cos 0 = adj Tan 0 = opp

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?
• 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

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

How do I find an angle?

obtuse

reflex

acute

Find the value of 0
• 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)

0

10cm

5cm

hyp

opp

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