Trigonometry Paper 2 Question 5

Trigonometry Overview Right Angled?Find Angle? Inverse: SOH CAH TOA Find Side?Given 2 sides Pythagoras Given 1 side only SOH CAH TOA Non-right Angled? Area Involved? Area = ½ │ a ││ b │ sinC Sine Rule? Find Side? a = b sinAsinB Find Angle? sinA = sinB ab

A 5 cm 10 cm Find angle A? Solution using CAH cosA = (5/10) A = cos -1 (5/10) = 60 o Solution using CAH cosA = (5/10) A = cos -1 (5/10) = 60 o hypotenuse Right angled triangle adjacent

x 10 cm 6 cm Find the length of x? Solution using Pythagoras 10 2 = x x = √(10 2 – 6 2 ) = √64 = 8 cm Solution using Pythagoras 10 2 = x x = √(10 2 – 6 2 ) = √64 = 8 cm Right angled triangle hypotenuse

60 o 4 cm x Find the length of x? Solution using SOH sin60 o = x/4 x = 4sin60 o = 2 √3 cm Solution using SOH sin60 o = x/4 x = 4sin60 o = 2 √3 cm hypotenuse Right angled triangle opposite

Find the area of the triangle, correct to the nearest whole number? 9 cm 70 o 8 cm Solution using Area = ½(a)(b)sinC Area = ½ (9)(8)sin70 o ≈ 34 cm 2 Solution using Area = ½(a)(b)sinC Area = ½ (9)(8)sin70 o ≈ 34 cm 2 Non-right angled triangle

If the area off the triangle is 24 cm 2 find the length of side x, correct to 1 decimal place? 8 cm 70 o x Solution using Area = ½(a)(b)sinC 24 = ½ (x)(8)sin70 o x = 2(24)/8sin70 o ≈ 6.4 Solution using Area = ½(a)(b)sinC 24 = ½ (x)(8)sin70 o x = 2(24)/8sin70 o ≈ 6.4 Non-right angled triangle

Find the size of angle A, correct to the nearest whole number? 15 cm 65 o 14 cm A sinA = sinB a b Non-right angled triangle

Find the length of side x, correct to 1 decimal place? 16 cm 55 o x 75 o a = b sinAsinB 50 o Non-right angled triangle

Trigonometry Overview Right Angled?Find Angle? Inverse: SOH CAH TOA Find Side?Given 2 sides Pythagoras Given 1 side only SOH CAH TOA Non-right Angled? Area Involved? Area = ½ │ a ││ b │ sinC Sine Rule? Find Side? a = b sinAsinB Find Angle? sinA = sinB ab