Question

Fie triunghiul dreptunghic abc cu m(a)=90 grade ,ad perpendiculara pe bc ,De(BC) ,dc=9cm si tgC=2 supra 3
a)Determinati lunigimile laturilor triunghiului
b)Calculati sin B + cos B
Ofer 35 de puncte!!!!!!

Answer 1

tg C =2/3
tgC= AD/DC
2/3= AD/9 =>AD= 2×9//3=18/3=6 cm
AD²=CD×BD
6²= 9×BD
36=9×BD
BD=36:9
BD =4 cm
BC =CD+BD =4+9 = 13 cm
In ∆ABC dr =>T cat
AB² =BD×BC
AB²= 4×13
AB²= 52
AB=√52
AB= 2√13
m
In ∆ABC dr =>T cat
AC²=CD×BC
AC² = 9×13
AC²= 117
AC=√117
AC= 3√13 cm

sin B = AC/BC = 3√13/13
coa B = AB/BC = 2√13/13
Sin B +cos B = 3√13/3+2√13/13= 5√13/13