Question

in triunghiul dreptunghic abc, m(a)=90° si ad perpendicular bc, d apartine bc se cunosc 2 segmente. a) bd=27cm si cd=48cm calculati bc ad ab ac
b)ac=40cm si cd=32cm se cer bc,bd,ab,ad

DAU FUNDA

Answer 1

Răspuns:

a) BC=75cm, AD=36cm, AB=45cm, AC=60cm;

b) se rezolva analog ...

Explicație pas cu pas:

BC=BD+CD=27+48=75, dUPA TEOREMA INALTIMEI AVEM: AD^2=BD*CD=27*48, De unde AD=RADICAL(27*48)=RADICAL(9*3*16*3)= 3*4*3=36, DECI AD=36.

aCUM FOLOSIM TEOREMA CATETEI: AB^2=BD*BC=27*75, DECI AB=RADICAL(27*75)=RADICAL(9*3*25*3)=3*5*3=45, DECI AB=45

ANALOG AFLAM CATETA AC: AC^2=CD*CB=48*75, DE UNDE AC=RADICAL(48*75)=RADICAL(16*3*25*3)=4*5*3=60, DECI AC=60