Question

In triunghiul ABC dreptunghic in A avem inaltimea AD=6 CM D apartine de bc si B=60 de grade calculati perimetrul​

Answer 1

Răspuns:

Explicație pas cu pas:

∡B=60°

AD= 6 cm (inaltime)

.....................................

P=?

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Demonstratie :

sin∡B= AD/AB

sin 60°=6/AB

sin 60°=√3/2

√3/2=²⁾6/AB

√3=12AB

AB= 12/√3=12√3/3=4√3cm

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tg ∡B= AC /AB

tg 60°=AC/4√3

tg60°=√3

√3=AC/4√3

AC= 4√3*√3

AC=4*3

AC= 12 cm

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teorema lui Pitagora

BC²=AC²+AB²

BC²=12²+(4√3)²

BC²=144+16*3

BC²=144+48

BC²=192

BC=√192

BC=8√3

-

P= AB+AC+BC

P=4√3+12+8√3

P=12√3+12

P= 12*(√3+1) cm ( perimetrul)