Question

triunghiul dreptunghic abc cu masura unghiului a=90 are tg B=0,75 si bc=30 cm. Calculati perimetrul triunghiului si functiile trigonometrice ale unghiurilor B si C

Answer 1

B
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A_____________C
tgB=AC/AB=75/100=3/4 =>AC=3AB/4
T.Pitagora : AC^2 + AB^2 = BC^2
9AB^2/16 + AB^2 = 900
25AB^2/16 = 900
25AB^2 = 900×16
AB^2 = (900×16)/25
AB=(30×4)/5 =>AB=24 =>AC=18
sinB=AC/BC=18/30=3/5
cosB=AB/BC=24/30=4/5
tgB - ip.
ctgB=AB/AC=24/18=4/3

sinC=AB/BC=4/5
cosC=AC/BC=3/5
tgC=AB/AC=4/3
ctgC=AC/AB=18/24=3/4