1. The General Triangle
Tuesday, 09 April 2019

2. The General Triangle C B A

3. The General Triangle a C B A

4. The General Triangle a C B b A

5. The General Triangle a C B c b A

6. The Sine Rule B
𝑎 sin 𝑎
= 𝑏 sin 𝑏
= 𝑐 sin 𝑐 a c C A b

7. Example
Find 𝑎 in the triangle below a
8 cm
27
110

8. Find c in the triangle below
Example
Find c in the triangle below c
7 cm
60
50

9. First we must find this angle using angles in a triangle angle = 86⁰
Example
Find 𝑥 in the triangle below x
10.6 cm
54
40
First we must find this angle using angles in a triangle angle = 86⁰

10. Find the size of angle B in the triangle below
Example
Find the size of angle B in the triangle below
15cm
120 A B C
6cm
Similar to the previous question the information provided only allows us to find angle C first

11. Find the size of angle A in the triangle below
Example
Find the size of angle A in the triangle below
24cm
70 A B C
27cm

12. The Cosine Rule A B C c a b Or

13. Example Find the length 𝑏 in the triangle below
8cm
112
5cm b

14. Example Find the length 𝑥 in the triangle below
9cm
64
10cm x

15. Example Find the length 𝑦 in the triangle below
7.5cm
48
12.3cm y

16. Example Find angle C 6 B C 7 5 A
Alternatively you could rearrange the cosine formula and use

17. Trigonometry Questions
Calculate the size of angle A in the triangle ABC
Calculate the length XY in the triangle XYZ
6 cm
4 cm A C B
59
4.6 cm Z X Y

18. 3. The figure is a pyramid on a square base ABCD
3. The figure is a pyramid on a square base ABCD. The edges of the base are 30cm
long and the height, EH, of the pyramid is 42cm. Find
the length of AC
the angle EAH E C D B A H

19. ABC, correct to the nearest degree.
4. Find angle P
5. A triangle has AB = 8cm, BC = 12cm and ACB = 25⁰ . Calculate the size of angle
ABC, correct to the nearest degree. 8 6 11 Q R P

20. 6. A port, B is 20 km north-east of a port, A.
A lighthouse, L, is 5 km from B on a bearing of 260⁰ from B.
Calculate the distance AL.
Calculate, to the nearest degree, the bearing of L from A.

21. 7. Find angle DCB in the shape below
8. Find Angle N A B C D
80
72 5 8 10
70º
9.7cm
10cm N

22. 9. Find the length of side f.
10. In triangle ABC where AB = 5cm, BC = 6cm and AC = 4.3cm. Work out the size
of the largest angle.
50º f
29 cm
28 cm