Question

ΔABC dr
m AB=9
BC=15

AC=?
sin < B=?
cos < B=?
tg ct

Answer 1

BC²=AC²+ AB²
15²= AC² + 9²                  ⇒ AC² =225 - 81 = 144  ; AC =√144 = 12 
sinB=AC/BC= 12 / 15 = 4/5
cosB= AB/ BC= 9 /15 = 3/5 
tgB= AC/AB= 12/9 = 4/3 
ctgB= AB/ AC= 9/12 = 3/4

Answer 2

$BC^{2}$ = $AC^{2}+ AB^{2}$
$225$= $AC^{2}$ + $81$     ⇔$AC^{2}$ =$225-81=144$ 
$AC= \sqrt{144}=12$ 
$sinB$ =  $\frac{AC}{BC}$ = $\frac{12}{15}$ $simplificam$ $cu$ $3$  = $\frac{4}{5}$
$cosB$ = $\frac{AB}{BC}$ = $\frac{9}{15} simplificam$ $cu$ $3$  = $\frac{3}{5}$ 
⇒ $tgB$= $\frac{AC}{AB}$= $\frac{12}{9}$ $simplificam$ $cu$ $3$  = $\frac{4}{3}$
⇒ $ctgB$= $\frac{AB}{AC}$  = $\frac{9}{12}$  = $\frac{3}{4}$