Trigonometry in Rightangled Triangles Module 8

Trigonometry  A method of calculating the length of a side Or size of an angle  Calculator required

SINE Ratio – find Opposite side A B C 30º 10.2cm x Sine30 = x 10.2 x = 10.2 x Sine30 x = 5.1cm Hypotenuse Opposite Sine = Opposite Hypotenuse

SINE Ratio – find Opposite side A B C 46º 8.4cm x Hypotenuse Opposite Sine46 = x 8.4 x = 8.4 x Sine46 x = ….cm Sine = Opposite Hypotenuse x = 6.04cm (3 sig fig)

SINE Ratio – find angle A B C xº 9.1cm 3.4cm Hypotenuse Opposite Sin x = Sin -1 (3.4÷9.1) = …º Sine = Opposite Hypotenuse <ABC = 21.9º (3 sig fig) Sin -1 – Shift Sin

SINE Ratio – find Hypotenuse A B C 32º x cm 3.2cm Hypotenuse Opposite Sin 32 = 3.2 x = …cm Sine = Opposite Hypotenuse BC = 6.04cm (3 sig fig) x = 3.2 Sin32

Cosine & Tangent?  Are TWO other ratios we can use  Similar process for calculating sides and angle  You now need to decide which ratio to use

SOHCAHTOA Silly Old Horace Caught A Haddock Trawling Off Afghanistan Sine = O H Cosine = A H Tangent = O A Cos Tan Sin

Ratios A B C xº 5cm 3cm Hypotenuse 4cm Opposite Adjacent Sin x= 3 5 Cos x= 4 5 Tan x= 3 4

Which ratio to use? A B C 32º 3.2 cm x cm Hypotenuse Opposite Adjacent SOH CAH TOA ? ? √ Tan32 = x 3.2 x = 3.2 x Tan32 x = ….cm x = 2.00 cm (3 sig fig) √

Which ratio to use? A B C 38º 2.6 cm Hypotenuse Opposite Adjacent SOH CAH TOA Cos38 = 2.6 x x = 2.6 / Cos38 x = 3.299….cm x = 3.30 cm (3 sig fig) x cm