Trigonometry

More documents

Recommendations

Info

Higher Mathematics Unit 2 – Mathematics 2EXAMPLE1. The triangular prism ABCDEF is shown below.EA10 cmCalculate the acute angle between:(a) The line AF and the plane ABCD.(b) AE and ABCD.(a) Start with a sketch:Oppositetana=Adjacent=3101(3 )−Aa = tan10 cm D10= 16. 699 ° (or 0.291 radians) (to 3 d. p .)NoteSince the angle is in a right-angled triangle, it must be acute (i.e. lie inthe first quadrant) and therefore we do not use a CAST diagram.(b) Again, make a sketch:b angle to beAcalculatedWe need to calculate the length of AC first using Pythagoras’s Theorem:C2 2AC = 10 + 66 cmA= 13610 cm DTherefore:EOppositetanb=3 cm Adjacent= 3C136AabF136 cmB3 cmE3 cmCFDC6 cm3 cm1 3( )−b = tan136= 14. 426 ° (or 0.252 radians) (to 3 d. p .)hsn.uk.netPage 94HSN22300
Higher Mathematics Unit 2 – Mathematics 2The angle between two planesThe angle a between planes P and Q is calculated by drawing a lineperpendicular to Q and then using basic trigonometry.PQaEXAMPLE2. ABCDEFGH is a cuboid with dimensions 12 × 8× 8 cm as shown below.HGEF8 cm8 cmA 12 cm B(a) Calculate the size of the angle between the planes AFGD and ABCD.(b) Calculate the size of the acute angle between the diagonal planesAFGD and BCHE.(a) Start with a sketch:FAa12 cm8 cmBDOppositetana=Adjacent=8121(2 )CNoteAngle GDC is the samesize as angle FAB−a = tan 3= 33. 690 ° (or 0.588 radians) (to 3 d. p .)(b) Again, make a sketch:EFTA• •BLet AF and BE intersect at T ATB is isosceles, so TAB = TBA ɵ = 33.690 °ATB = 180° − ( 33. 690° + 33.690°)= 112.620°NoteThe angle could alsohave been calculatedusing rectangle DCGHSo the acute angle is:BTF = ATE = 180° − 112.620°= 67. 380 ° (or 1.176 radians) (to 3 d. p .)hsn.uk.netPage 95HSN22300
Page 1: hsn.uk.netHigherMathematicsUNIT 2 O
Page 4 and 5: Higher Mathematics Unit 2 - Mathema
Page 12: Higher Mathematics Unit 2 - Mathema

Trigonometry

Create successful ePaper yourself

Delete template?

Save as template?