Question

In triunghiul dreptunghic LMN cu ipotenuza MN MN=30 cos M =2/15.Calculati perimetru si aria triunghiului LMN.

Answer 1

Deci vei avea LM= cosMxMN si afli NL prin Pitagora si apoi calculezi perimetrul si aria=NL x ML

Answer 2

cosM = $\frac{LM}{MN} = \frac{2}{15} <=> \frac{LM}{30} = \frac{2}{15} => LM = 4$ 

Pitagora : $MN^{2} = ML^{2} + LN^{2} <=> 900 = 16 + LN^{2} <=> LN^{2} = 884 <=>$ $<=> LN = 2 \sqrt{221}$

   P = MN + LM + LN = 30 + 4 + 2√221 => P = 34 + 2√221

  A = $\frac{cateta*cateta}{2} = \frac{LM*LN}{2} = \frac{4*2 \sqrt{221} }{2} = 4 \sqrt{221}$