2. 1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use Trigonometry Finding Sides Stage 6 - Year 11 General Mathematics Preliminary

3. 2 13.2 Calculating Trig Ratios (1/11) You can use your calculator to find trigonometric ratios. When finding the angle we need to show working Example: Sin θ = 0.649 θ = Sin -1 (0.649) = 40.4662 o Use DMS or o ’ ’’ = 40 o 27’ 58’’ Degrees Minutes Seconds

4. 3 13.3 The Trigonometric Ratios (2/11) α OppositeAdjacentHypotenuse

5. 4 The Trigonometric Ratios (3/11) OppositeAdjacentHypotenuse β

6. 5 The Trigonometric Ratios (4/11) θ o h a S Sin θ = C Cos θ = T Tan θ = ohoh ahah oaoa S 0 H C A H T 0 A ome ld ags an lways ide heir ld ge

7. 6 The Trigonometric Ratios (5/11) θ o h a θ o h a

8. 7 The Trigonometric Ratios (6/11) 45 o 13cm x h Cos 45 o = x 13 a ah Because we have a and h Cos we must use Cos. x13 13x x = 13 x Cos 45 o ≈ 9.192 388 ≈ 9.2cm

9. 8 The Trigonometric Ratios (7/11) 35 o 10m x h Sin 35 o = x 10 o oh Because we have o and h Sin we must use Sin. x10 10x x = 10 x Sin 35 o ≈ 5.735 764 ≈ 5.7m

10. 9 Finding an Unknown Side (8/11) 40 o 12m p a Tan 40 o = p 12 o oa Because we have o and a Tan we must use Tan. x12 12x x = 12 x Tan 40 o ≈ 10.069 195 ≈ 10.1m

11. 10 Finding an Unknown Side (9/11) 50 o 3m d h Sin 50 o = 3d3d o oh Because we have o and h Sin we must use Sin. x d d x d = 3 ÷ Sin 50 o ≈ 3.916 221 ≈ 3.9 m d x Sin 50 o = 3 ÷ Sin 50 o

12. 11 Finding an Unknown Side (10/11) 60 o 7m m a Cos 60 o = 7m7m h ah Because we have a and h Cos we must use Cos. x m m x m = 7 ÷ Cos 60 o ≈ 14.0 m m x Cos 60 o = 7 ÷ Cos 60 o

13. 12 Finding an Unknown Side (11/11) 60 o 7m w a Tan 60 o = 10 m o oa Because we have o and a Tan we must use Tan. x w w x w = 10 ÷ Tan 60 o ≈ 5.773 502 ≈ 5.8 m w x Tan 60 o = 10 ÷ Tan 60 o