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Sa se afle lungimea diag AC a unui romb ABCD in carese stie AD=15cm si sinÂ=1/5

Răspuns :

AD=15
sinA=[tex] \frac{1}{5} [/tex]

sinA1=[tex] \frac{BO}{AB} [/tex]
sinA2=[tex] \frac{OD}{AD} [/tex]

[tex] \frac{BO}{AB} + \frac{OD}{AD}= \frac{BD}{15} [/tex]
AB=AD

[tex] \frac{BD}{15} = \frac{1}{5} [/tex]
BD=3

ABD e triunghi isoscel, deci AO il imparte pe BD in jumatate

aplicam teorema lui Pitagora in triunghiul dreptunghic AOB

[tex] 1,5^{2}+ AO^{2}= 15^{2} [/tex]
AO=10⇒OC=10 

AC=AO+OC
AC=10·2
AC=20