1. 1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use Trigonometry in 3 Dimensions Stage 6 - Year 11 Mathematic Extension 1 (Preliminary)

2. 2 It is the same as normal trigonometry accept in more than one plane. End of Slide 0 X Y Z 35 o h θoθo 4.2 cm 1.5 cm tan 35 o = h 4.2 x4.2 4.2x h = 4.2 x tan 35 o ≈ 2.9 cm Find h

3. 3 It is the same as normal trigonometry accept in more than one plane. End of Slide 0 X Y Z 35 o h θoθo 4.2 cm 1.5 cm tan θ o = 2.9 1.5 2.9 tan θ o = 2.9 1.5 tan -1 ( ) θ o = 2.9 1.5 tan -1 ( ) ≈ 62.6501.. o ≈ 62 o 39’ Find θ

4. 4 End of Show θoθo 5m 8m 12m 1. Find XY X Y XY 2 = 5 2 + 12 2 XY 2 = 169 XY = 13 2. Find θ 13 8 tan θ o = 8 13 tan θ o = 8 13 tan -1 ( ) θ o = 8 13 tan -1 ( ) ≈ 31.6075 o ≈ 31 o 36’27’’ θoθo