1. Trigonometry – Angles & Lengths – Demonstration
This resource provides animated demonstrations of the mathematical method.
Check animations and delete slides not needed for your class.

2. θ Hypotenuse Opposite Adjacent A right-angled triangle has 4 parts.
θ = Theta is either angle.
Hypotenuse
Opposite θ
Adjacent
Hypotenuse – always opposite the right-angle & always longest.
Opposite – always opposite θ.
Adjacent – next to θ.

3. SOH CAH TOA 𝑥 (H) 7 cm 62° (O) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find O.
(so cover O)
(H)
7 cm
𝑆𝑖𝑛 θ ×𝐻 =𝑂
62° 𝑥
𝑆𝑖𝑛 62×7=𝑂
=6.18 cm
(O)

4. SOH CAH TOA 𝑥 (H) 34° 12 cm (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find H.
(so cover H)
(H) 𝑥
𝐴 𝐶𝑜𝑠 θ =𝐻
34°
12 𝐶𝑜𝑠 34 =𝐻
=14.47 cm
12 cm
(A)

5. SOH CAH TOA 𝑥 (O) (A) 4 cm 52° 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find O.
(so cover O) 𝑥
(O)
𝑇𝑎𝑛 θ×𝐴 =𝑂
(A)
4 cm
52°
𝑇𝑎𝑛 52×4=𝑂
=5.12 cm

6. SOH CAH TOA 𝑥 (H) 6 cm 5 cm (O) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find Sin θ.
(so cover Sin θ)
(H)
𝑆𝑖𝑛 θ= 𝑂 𝐻
𝑆𝑖𝑛 𝑥= 5 6
6 cm 𝑥
𝑆𝑖𝑛 −
5 cm 𝑥=
=56.44°
(O)

7. SOH CAH TOA 𝑥 (H) 17 cm 14 cm (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find Cos θ.
(so cover Cos θ)
(H)
17 cm
𝐶𝑜𝑠 θ= 𝐴 𝐻
𝐶𝑜𝑠 𝑥= 14 17 𝑥
𝐶𝑜𝑠 − 𝑥=
=34.56°
14 cm
(A)

8. SOH CAH TOA 𝑥 (O) 5 cm 3 cm (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find Tan θ.
(so cover Tan θ)
(O)
5 cm
𝑇𝑎𝑛 θ= 𝑂 𝐴
𝑇𝑎𝑛 𝑥= 5 3
3 cm
𝑇𝑎𝑛 − 𝑥 𝑥=
=59.04°
(A)

9. SOH CAH TOA 𝑥 7 cm (O) 9 cm (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find Sin θ.
(so cover Sin θ)
7 cm
(O)
𝑆𝑖𝑛 θ= 𝑂 𝐻
𝑆𝑖𝑛 𝑥= 7 9 𝑥
𝑆𝑖𝑛 −
9 cm 𝑥=
=51.06°
(H)

10. SOH CAH TOA 𝑥 (O) 11 cm 34° (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find A.
(so cover A)
(O)
𝑂 𝑇𝑎𝑛 θ =𝐴
11 cm
11 𝑇𝑎𝑛 34 =𝐴
34°
=16.31 cm 𝑥
(A)

11. SOH CAH TOA 𝑥 (H) 13 cm 37° (A) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find A.
(so cover A)
(H)
13 cm
𝐶𝑜𝑠 θ×𝐻 =𝐴
37°
𝐶𝑜𝑠 37×13=𝐴
=10.38 cm 𝑥
(A)

12. SOH CAH TOA 𝑥 (A) 5 cm 14 cm (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find Cos θ.
(so cover Cos θ)
(A)
5 cm
𝐶𝑜𝑠 θ= 𝐴 𝐻
𝐶𝑜𝑠 𝑥= 5 14 𝑥
𝐶𝑜𝑠 − 𝑥=
=69.08°
14 cm
(H)

13. SOH CAH TOA 𝑥 26 cm (O) 49° (H) 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find H.
(so cover H)
26 cm
𝑂 𝑆𝑖𝑛 θ
(O) =𝐻
49°
26 𝑆𝑖𝑛 =𝐻 𝑥
=34.45 cm
(H)

14. SOH CAH TOA 𝑥 (A) (O) 7 cm 4 cm 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Find the value of 𝑥 to 2dp.
We want to find Tan θ.
(so cover Tan θ)
(A)
(O)
𝑇𝑎𝑛 θ= 𝑂 𝐴
𝑇𝑎𝑛 𝑥= 7 4
7 cm
4 cm 𝑥
𝑇𝑎𝑛 − 𝑥=
=60.26°

15. SOH CAH TOA 𝑥 𝑥 𝑥 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Calculate 𝑥 for these three triangles. (2dp)
10 cm
36° 𝑥 𝑥 𝑥
8 cm
9 cm
21°
14 cm

16. SOH CAH TOA 𝑥 𝑥 𝑥 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Calculate 𝑥 for these three triangles. (2dp)
10 cm
36°
𝑆𝑂𝐻
𝑇𝑂𝐴 𝑥 𝑥 𝑥
8 cm
9 cm
𝐶𝐴𝐻
21°
14 cm

17. SOH CAH TOA 𝑥 𝑥 𝑥 𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝 𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝 𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O H A H
𝑆𝑖𝑛 θ= 𝑂𝑝𝑝 𝐻𝑦𝑝
𝐶𝑜𝑠 θ= 𝐴𝑑𝑗 𝐻𝑦𝑝
𝑇𝑎𝑛 θ= 𝑂𝑝𝑝 𝐴𝑑𝑗 O
Sin θ H A
Cos θ H O
Tan θ A
Calculate 𝑥 for these three triangles. (2dp)
𝑥=13.07 𝑐𝑚
10 cm
36°
𝑆𝑂𝐻
𝑇𝑂𝐴 𝑥 𝑥 𝑥
8 cm
9 cm
𝐶𝐴𝐻
21°
𝑥=12.39 𝑐𝑚
𝑥=53.13°
14 cm

19. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to