1. A = Cos o x H
Cosine Rule
To find an adjacent side we need 1 side (hypotenuse) and the included angle.
9 cm
12 cm
60°
75° a a
A = Cos ° x H
A = Cos 75° x 12
A = x 12
A = 3.1 cm
A = Cos ° x H
A = Cos 60° x 9
A = 0.5 x 9
A = 4.5 cm

2. Cos o = A ÷ H
Cosine Rule
To find an unknown angle we need 2 sides the adjacent and the hypotenuse
5 cm
15 cm x° y°
2.5 cm
12cm
Cos ° = A ÷ H
Cos ° = 12 ÷ 15
Cos ° = 0.8
Shift (Inv) (2ndF) Cos = 36.9°
Cos ° = O ÷ H
Cos° = 2.5 ÷ 5
Cos° = 0.5
Shift (Inv) (2ndF) Cos = 60°

3. O = Sin o x H
Sine Rule
To find an opposite side we need 1 side (hypotenuse) and the included angle.
5 cm
10 cm o o
30°
75°
O = Sin ° x H
O = Sin 30° x 5
O = 0.5 x 5
O = 2.5 cm
O = Sin ° x H
O = Sin 75° x 10
O = x 10
O = 9.7cm

4. Sin o = O ÷ H
Sine Rule
To find an unknown angle we need 2 sides the opposite and the hypotenuse
5 cm
15 cm
2.5 cm
12cm x° y°
Sin ° = A ÷ H
Sin ° = 12 ÷ 15
Sin ° = 0.8
Shift (Inv) (2ndF) Sin = 53.1°
Sin ° = O ÷ H
Sin ° = 2.5 ÷ 5
Sin ° = 0.5
Shift (Inv) (2ndF) Sin = 30°

5. To find an unknown angle we need 2 sides the opposite and the adjacent
Tan o = O ÷ A
Tangent Rule
To find an unknown angle we need 2 sides the opposite and the adjacent
2.5 cm
12cm x° y°
5 cm
15 cm
Tan ° = A ÷ H
Tan ° = 12 ÷ 15
Tan ° = 0.8
Shift (Inv) (2ndF) Tan = 38.6°
Tan ° = O ÷ H
Sin ° = 2.5 ÷ 5
Sin ° = 0.5
Shift (Inv) (2ndF) Tan = 26.6°

6. O = Tan o x A
Tangent Rule
To find an opposite side we need 1 side (adjacent) and the included angle. a a
45°
75°
9 cm
6 cm
O = Tan ° x A
O = Tan 45° x 9
O = 1 x 9
O = 9 cm
A = Tan ° x H
A = Tan 75° x 6
A = x 6
A = 22.4 cm