1. Right Angled Triangles
The key points

2. 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

4. Find the length of ‘j’ To find ‘j’, use P.T. Label the hypotenuse.
j = 9 cm
15cm
hyp
12cm j

5. Any other sort of questions?
If it is then the hypotenuse is 6cm (longest side) and P.T. will work.
= = 41
62 = 36
so = 62
P.T. does NOT work so no right angle
Is this triangle right- angled?
Hyp?
4cm
6cm
5cm

6. So that’s it for right angled triangles?

7. Don’t forget trigonometry. (Worth big marks)
Unfortunately not
Don’t forget trigonometry.
(Worth big marks)

8. 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.

9. 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.

10. Then pick your equation.
Sin 0 = opp Cos 0 = adj Tan 0 = opp
hyp hyp adj
0 is the Greek letter ‘theta’ which denotes an angle.

11. 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.

12. What?
Find the value of ‘f’
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
10cm
‘f ’
hyp
opp
300
adj

13. 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

14. How do I find an angle?
obtuse
reflex
acute

15. 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)
10cm
5cm
hyp
adj
opp

16. 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

17. I don’t want to have to say
I hope this helped
I don’t want to have to say

18. That’s all folks!
The end