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 = 0.258819045 x 12 A = 3.1 cm A = Cos ° x H A = Cos 60° x 9 A = 0.5 x 9 A = 4.5 cm

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-1 0.8 = 36.9° Cos ° = O ÷ H Cos° = 2.5 ÷ 5 Cos° = 0.5 Shift (Inv) (2ndF) Cos-1 0.5 = 60°

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 = 0.965925826 x 10 O = 9.7cm

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-1 0.8 = 53.1° Sin ° = O ÷ H Sin ° = 2.5 ÷ 5 Sin ° = 0.5 Shift (Inv) (2ndF) Sin-1 0.5 = 30°

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-1 0.8 = 38.6° Tan ° = O ÷ H Sin ° = 2.5 ÷ 5 Sin ° = 0.5 Shift (Inv) (2ndF) Tan-1 0.5 = 26.6°

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 = 3.732050808 x 6 A = 22.4 cm