Trigonometry means “triangle” and “measurement”. Adjacent Opposite x°x°x°x° hypotenuse We will be using right-angled triangles. The Tan Ratio Trigonometry

60° 12 m Adjacent Opposite hypotenuse Copy this! The Tan Ratio Finding the ‘Opposite’ side

Tan x° = Opp Adj Tan 60° = Opp 12 = Opp12 x Tan 60° Opp =12 x Tan 60°= 20.8m (1 d.p.) Copy this! The Tan Ratio Finding the ‘Opposite’ side O TanA

47° 20 m Adjacent Opposite hypotenuse Copy this! The Tan Ratio Finding the ‘Opposite’ side

Tan x° = Opp Adj Tan 47° = Opp 20 = Opp20 x Tan 47° Opp =20 x Tan 47°= 21.4m (1 d.p.) Copy this! The Tan Ratio Finding the ‘Opposite’ side O TanA

Use the tan ratio to find the height h of the tree to 1 decimal place. 47 o 8m rod The Tan Ratio Trigonometry Tan x° = Opp Adj Tan 47° = h 8 8 x Tan 47°= h 8 x Tan 47°= 8.6m (1 d.p.) h O TanA

Use the tan ratio to calculate how far the ladder is away from the building. 45 o 12m ladder d m The Tan Ratio Trigonometry Tan x° = Opp Adj Tan 45° = 12 d d x tan 45º = 12 d = 12 tan 45º = 12m O TanA

6o6o Aeroplane 1.58 km Lennoxtown Airport Q1.An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present. It is at a height of 1.58 km above the ground. It ‘s angle of descent is 6 o. How far is it from the airport to Lennoxtown? Example 2 The Tan Ratio Trigonometry Tan x° = Opp Adj Tan 6° = 1.58 a a = 1.58 tan 6º = 15.03km (2 d.p) ? O TanA

Using Tan to calculate angles

18 12 Example x°x° Tan x° = Opp Adj Hyp 12m Tan x° = Adj 18m Calculate the tan x o ratio Q P R The TAN Ratio Calculating the angle

The TAN Ratio Calculating the angle How do we find x°? We need to use Tan ⁻ ¹ on the calculator. 2 nd Tan ⁻ ¹is written above Tan Tan ⁻ ¹ To get this press Tan Followed by Calculate the size of angle x o Tan x° =

x = Tan ⁻ ¹ = 56.3° (1 d.p.) 2 nd Tan Tan ⁻ ¹ Press Enter = The TAN Ratio Calculating the angle Tan x° =

Process 1.Identify Hyp, Opp and Adj 2.Write down ratio Tan x o = Opp Adj 3.Calculate x o 2 nd Tan Tan ⁻ ¹ The TAN Ratio Calculating the angle

Use the tan ratio to calculate the angle that the support wire makes with the ground. xoxo 11m 4 m The TAN Ratio Calculating the angle hyp opp adj Tan x° = Opp Adj 11 4 Tan x° =

11 Tan x° = 4 The TAN Ratio Calculating the angle 2 nd Tan Tan ⁻ ¹ Press Enter = 11 4 x = Tan ⁻ ¹ 11 = 70.02° (2 d.p.) 4

The Sine Ratio x°x°x°x° Sin x° = O p p o s i t e Opp Hyp h y p o t e n u s e Trigonometry

Example 34° Sin x° = Opp Hyp h 11cm Sin 34° = h 11 = h 11 x Sin 34° h =11 x Sin 34°= 6.2cm (1 d.p.) Find the height h The Sine Ratio Trigonometry O SinH Adj

The support rope is 11.7m long. The angle between the rope and ground is 70 o. Use the sine ratio to calculate the height of the flag pole. 70 o h 11.7m The Sine Ratio Trigonometry hyp opp adj Sin x° = Opp Hyp Sin 70° = h 11.7 O SinH = h11.7 x Sin 70° h =11.7 x Sin 70°= 11.0cm (1 d.p.)

Example 72° Sin x° = Opp Hyp Sin 72° = 5 r r = 5.3 km 5km AB C r A road AB is right angled at B. The road BC is 5 km. Calculate the length of the new road AC. The Sine Ratio Trigonometry Hyp Opp Adj O SinH 5 Sin 72º

Using Sin to calculate angles

Using Sine ratio to find an angle Example x°x°x°x° Sin x° = Opp Hyp 6m 9m Sin x° = 6 9 Find the x o Trigonometry Adj

=Sin x° How do we find x°? We need to use Sin ⁻ ¹ on the calculator. 2 nd Sin ⁻ ¹is written above Sin Sin ⁻ ¹ To get this press Sin Followed by Using Sine ratio to find an angle Trigonometry 6 9

x = Sin ⁻ ¹ = 41.8° (1 d.p.) =Sin x° 2 nd Sin Sin ⁻ ¹ Press Enter = 6 9 Using Sine ratio to find an angle Trigonometry () ()

Use the sine ratio to find the angle of the ramp. xoxo 10m 20 m Using Sine ratio to find an angle Trigonometry

The Cosine Ratio Cos x° = Adjacent Adj x°x°x°x° Hyp h y p o t e n u s e Trigonometry opposite

Example 40° Cos x° = Opp Adj Hyp b 35mm Cos 40° = b 35 = b35 x Cos 40° b =35 x Cos 40°= 26.8mm (1 d.p.) Adj Find the length b The Cosine Ratio Trigonometry A CosH

Example 33° Cos x° = Opp Adj Hyp 26 c Cos 33° = 26 c = b c= 31.0mm (1 d.p.) Adj Find the length c The Cosine Ratio Trigonometry A CosH c = 26 cos 33

Using Cos to calculate angles

The Cosine Ratio Example x°x°x°x° Cos x° = Opp Adj Hyp 45cm Cos x° = = (3 d.p.)Cos x° x = Cos ⁻ ¹0.756 =41° Adj 34cm Trigonometry Find the angle x o

Sin x° = Opp Hyp Cos x° = Adj Hyp Tan x° = Opp Adj C A HT O AS O H Trigonometry Mixed Problems

S O H C A H T O A Copy this! 1. Write down Process Identify what you want to find what you know Trigonometry Mixed Problems

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Past Paper Type Questions S O H C A H T O A Trigonometry

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Past Paper Type Questions S O H C A H T O A Trigonometry

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