The General Triangle Tuesday, 09 April 2019

The General Triangle C B A

The General Triangle a C B A

The General Triangle a C B b A

The General Triangle a C B c b A

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

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

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

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

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

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

The Cosine Rule A B C c a b Or

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

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

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

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

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

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

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

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.

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

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