Trigonometry rules 14 December 2021 The General Triangle

Trigonometry rules 14 December 2021

The General Triangle B A C

The General Triangle B A a C

The General Triangle a B b A C

The General Triangle a B c b A C

The Sine Rule B a c A b C

• 8 cm a 27 110

Example Find c in the triangle below c 60 7 cm 50

• 10. 6 cm 54 x 40 First we must find this angle using angles in a triangle = 86⁰

• 84 12 cm 63 33 b

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

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

Example Find the size of angle R in the triangle below P 18. 5 cm 10. 5 cm R 85 Q

The Area of a triangle B a c A C b

Example Find the area of triangle ABC A 8 cm 114 B 6 cm C

C 5 cm A 7 cm B

Example (i) Find the length AB (ii) Hence find the area of the triangle. C (i) 5 cm 45 A 63 (ii) B

Example Find the area of triangle below First we must find this angle using the sine rule 12 cm 9 cm

Questions 1. Find the length of the lettered lengths for each of the following (a) (b) (c)

2. Find the size of the lettered angles for each of the following (a) (b)

5. Calculate the area for each of the following triangles (a) 9 cm 60° 6 cm (b) 34 cm 40° 57 cm

6. (a) Work out the size of angle A in the triangle below B 10 cm 20° A 15 cm (b) Hence find the area of triangle ABC C

7. Work out the area of the triangle drawn below 25° 80° 17 cm