Question

Triunghi dreptunghic ABC , m(<A)=90 , AD _l_ BC , D apartine ( BC ) ,DB = 9 cm si AB = 15 cm . Calculati : 

a) lungimile segmentelor AD si DC 
b) cos (<DAC)

Answer 1

ΔABC, mas<A=90
[AD] _|_ [BC]
[AD]-h

ΔABD, mas<D=90
AD²=AB²+BD²=15²+9²=225+81= 306   =>AD=3√34

ΔABC, mas<A=90
AD²=BD*DC

306=9*DC  =>DC=306/9= 34

BC=BD+DC=9+34= 43

AC²=BC² -AB²= 43² -15² = 1849-225= 1624   =>AC=2√406

ADC, mas<D=90
cos<DAC=AD/AC=  3√34/2√406= 3√13804/2*406=

=3 * 2√3451/2 *406= 3√3451/406