VRAE oor vraestel 2: 3D trig woordsom

Hi Annette

Dankie vir jou som. Dis so 'n goeie een, ek gaan vir jou 'n video ook maak! Click hier om dit te kyk (",)

Breek altyd jou 3D prentjie in aparte driehoeke op - dit maak die som soveel makliker.

a)

$table row cell In space increment APC end cell row cell straight A with hat on top equals 90 to the power of o left parenthesis gegee right parenthesis end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row cell t a n alpha end cell equals cell t over a equals fraction numerator A P over denominator A C end fraction end cell row cell A C tan alpha end cell equals cell A P end cell row cell A C end cell equals cell fraction numerator A P over denominator tan alpha end fraction end cell end table end cell end table$

$table row cell I n space increment A B C end cell row cell c o s A straight C with hat on top straight B equals a over s end cell row cell c o s A straight C with hat on top straight B equals fraction numerator A C over denominator B C end fraction end cell row cell equals open parentheses fraction numerator A P over denominator t a n alpha end fraction close parentheses divided by open parentheses fraction numerator B Q over denominator t a n beta end fraction close parentheses end cell row cell equals fraction numerator up diagonal strike A P end strike over denominator t a n alpha end fraction cross times fraction numerator t a n beta over denominator up diagonal strike B Q end strike end fraction space space space space space space space space space space space space space space space left parenthesis A P equals B Q space g e g e e right parenthesis end cell row cell equals fraction numerator t a n beta over denominator t a n alpha end fraction end cell end table$

$table row cell In space increment CBQ end cell row cell straight B with hat on top equals 90 to the power of o left parenthesis gegee right parenthesis end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row cell t a n beta end cell equals cell t over a equals fraction numerator B Q over denominator C B end fraction end cell row cell C B tan beta end cell equals cell B Q end cell row cell C B end cell equals cell fraction numerator B Q over denominator tan beta end fraction end cell end table end cell end table$

bi)

$table row cell uit space straight a right parenthesis end cell row cell c o s A straight C with hat on top straight B equals fraction numerator t a n beta over denominator t a n alpha end fraction end cell row cell c o s A straight C with hat on top straight B equals fraction numerator t a n 17.8 to the power of straight o over denominator t a n 31.4 to the power of straight o end fraction end cell row cell c o s A straight C with hat on top straight B equals 0.525988 end cell row cell straight A straight C with hat on top straight B equals 58.265 end cell row cell straight A straight C with hat on top straight B almost equal to 58.27 to the power of straight o end cell end table$

bii)

$table row cell In space increment ABC end cell row cell t a n space A straight C with hat on top straight B equals t over a equals fraction numerator A B over denominator A C end fraction end cell row cell t a n space 58.265 equals fraction numerator 42 over denominator A C end fraction end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell fraction numerator 42 over denominator t a n space 58.265 to the power of o end fraction end cell row blank equals cell 25.975 m end cell end table end cell end table$

$table row cell In space increment APC end cell row cell t a n space alpha equals t over a end cell row cell t a n space 31.4 to the power of o equals fraction numerator P A over denominator A C end fraction end cell row cell A C t a n space 31.4 to the power of o equals P A end cell row cell P A equals open parentheses 25.975 close parentheses t a n 31.4 to the power of o end cell row cell equals 15.855 end cell row cell P A equals B Q almost equal to 15.9 m end cell end table$