Trigonometry in Rightangled Triangles Module 8 Trigonometry o

Trigonometry in Rightangled Triangles Module 8

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

SINE Ratio – find Opposite side Sine = Opposite Hypotenuse x = 10. 2 x Sine 30 x = 5. 1 cm Opposite Sine 30 = x 10. 2 C Hypotenuse x 10. 2 cm 30º A B

SINE Ratio – find Opposite side Sine = Opposite Hypotenuse Opposite Sine 46 = x 8. 4 C Hypotenuse x 8. 4 cm 46º A x = 8. 4 x Sine 46 x = 6. 04245…. cm x = 6. 04 cm (3 sig fig) B

SINE Ratio – find angle Sin-1 – Shift Sin 3. 4 cm C Opposite Sine = Opposite Hypotenuse Sin x = 3. 4 9. 1 A Sin-1 (3. 4÷ 9. 1) = 21. 939…º <ABC = 21. 9º (3 sig fig) Hypotenuse 9. 1 cm xº B

SINE Ratio – find Hypotenuse x = 3. 2 Sin 32 3. 2 cm C Opposite Sine = Opposite Hypotenuse Sin 32 = 3. 2 x A = 6. 0386…cm BC = 6. 04 cm (3 sig fig) Hypotenuse x cm 32º B

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

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

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

Which ratio to use? C x cm Hypotenuse Opposite Tan 32 = x 3. 2 x = 1. 9995…. cm x = 2. 00 cm (3 sig fig) A x = 3. 2 x Tan 32 Adjacent 32º 3. 2 cm SOH √ TOA ? √ ? CAH B

Which ratio to use? C x = 2. 6 / Cos 38 Hypotenuse Opposite Cos 38 = 2. 6 x x = 3. 299…. cm x = 3. 30 cm (3 sig fig) x cm A Adjacent 38º 2. 6 cm SOH CAH TOA B