Trigonometry

Paper 2Question 5

TrigonometryOverview

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 sinA sinB

Find Angle?sinA = sinB a b

A5 cm

10 cm

Find angle A?

Solution using CAHcosA = (5/10)

A = cos-1 (5/10) = 60o

hypotenuseRight angled triangle

adjacent

x

10 cm6 cm

Find the length of x?

Solution using Pythagoras102 = x2 + 62

x = √(102 – 62) = √64 = 8 cm

Right angled triangle

hypotenuse

60o

4 cm x

Find the length of x?

Solution using SOHsin60o = x/4

x = 4sin60o = 2√3 cm

hypotenuse

Right angled triangle

opposite

Find the area of the triangle, correct to the nearest whole number?

9 cm

70o

8 cm

Solution using Area = ½(a)(b)sinCArea = ½ (9)(8)sin70o ≈ 34 cm2

Non-right angled triangle

If the area off the triangle is 24 cm2 find the length of side x, correct to 1 decimal place?

8 cm

70o

x

Solution using Area = ½(a)(b)sinC24 = ½ (x)(8)sin70o

x = 2(24)/8sin70o ≈ 6.4

Non-right angled triangle

Find the size of angle A, correct to the nearest whole number?

15 cm

65o

14 cm

A

sinA = sinB a b

SolutionsinA/14 = sin65o/15sinA = 14sin65o/15

A = sin-1(14sin65o/15) o

Non-right angled triangle

Find the length of side x, correct to 1 decimal place?

16 cm

55o

x75o

a = b sinA sinB

Solutionx/sin50o = 16/sin75o

X = 16sin50o/sin75o 12.7

50oNon-right angled triangle

TrigonometryOverview

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 sinA sinB

Find Angle?sinA = sinB a b