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3-Dimensional Pythagoras & Trigonometry

3-Dimensional Pythagoras & Trigonometry. C. Cuboid Question. H. G. D. 6cm. C. E. F. 3cm. 6cm. A. 5cm. B. B. A. 5cm. Find Length AG. AC = √ 5 2 +6 2 = 7.8cm. First: Find length AC using Pythagoras. 3-Dimensional Pythagoras & Trigonometry. H. G. D. C. E. F. 3cm. 3cm.

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3-Dimensional Pythagoras & Trigonometry

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  1. 3-Dimensional Pythagoras & Trigonometry C Cuboid Question H G D 6cm C E F 3cm 6cm A 5cm B B A 5cm Find Length AG AC = √52+62 = 7.8cm First: Find length AC using Pythagoras

  2. 3-Dimensional Pythagoras & Trigonometry H G D C E F 3cm 3cm 6cm A 5cm B 7.8cm Next: Find Length AG AG = √32+7.82 = 8.4cm

  3. 3-Dimensional Pythagoras & Trigonometry Find Angle CAG H G D C E F 3cm 3cm 6cm A 5cm B 7.8cm Find length AC as before then find the angle as: 3 7.8 tan-1 = 21o

  4. 3-Dimensional Pythagoras & Trigonometry Square Based Pyramid Question This is a square based pyramid, where the lengths of the sides of the square are 20.6cm and the height is 14.75cm X is the middle of the square base E Find Length AE 14.75 D C X 20.6cm A B 20.6cm

  5. 3-Dimensional Pythagoras & Trigonometry First: Find length AC using Pythagoras Find Length AE C E 20.6cm 14.75 D C A B 20.6cm X 20.6cm AG = √20.62+20.62 = 29.1cm A B 20.6cm

  6. 3-Dimensional Pythagoras & Trigonometry Next: Find Length AE using Pythagoras E E 14.75cm 14.75 D C 14.6cm A X X Note: ½ of AC ½ x 29.1 = 14.6 29.1cm AG = √14.62+14.752 = 20.8cm A B 20.6cm

  7. 3-Dimensional Pythagoras & Trigonometry Find the angle AE makes with the base E E 14.75cm 14.75 D C 14.6cm A X A X 29.1cm 14.75 14.6 tan-1 = 45o A B 20.6cm Angles given to a suitable degree of accuracy To the nearest whole number

  8. 3-Dimensional Pythagoras & Trigonometry Find the length EM where M is the midpoint of BC Make triangle EXM E E 14.75cm 14.75 D C X M X M 10.3cm 20.6cm AG = √20.62+14.752 = 25.3cm A B 20.6cm Note: ½ of BC ½ x 20.6 = 10.3

  9. 3-Dimensional Pythagoras & Trigonometry Find the angle that the face EBC makes with the base E E 14.75 14.75 D C X X M 10.3cm M 10.3cm 14.75 10.3 A tan-1 B = 55o

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