Question

Triunghiul ABC este dreptunghic in A. Se stie ca tgB=3/4 si BC=15

a)Pabc
b)fct trigo alr ung B

Answer 1

tgB=3/4=AC/AB (ipoteza)

4AC=3AB
AC^2+AB^2=15^2 (pitagora)

16AC^2=9AB^2
9AB^2/16 + AB^2=15^2
AB^2 x 25/16 = 15^2

AB=12
AC=9
perimetru ABC
P=AB+BC+AC=12+15+9
P=36

sinB=AC/BC=9/15=3/5
cosB=AB/BC=12/15=4/5
tgB=3/4
ctgB=4/3
secB=1/cosB = 5/4
cosecB=1/sinB=5/3