Question

daca un triunghi drep. are o cateta de 12cm si unghiul alăturat ei de 30°, are perimetrul deee?

Answer 1

Notam ABC triunghiul
m(<BCA)=30⁰
cos 30⁰=√3/2
12/BC=√3/2
BC=12×2/√3=24√3/3=8√3

sin 30⁰=1/2
AB/8√3=1/2
AB=8√3/2=4√3
P=4√3+8√3+12=12(√3+1) cm

Answer 2

P=a+b+c
sin30°=1\2=a\c
2a=c
tg30°=√3\2=a\b
b=$\dfrac{2}{\sqrt{3}}a$
a=12cm
$P=a+\dfrac{2}{\sqrt{3}}a+2a=a\left(3+\dfrac{2}{\sqrt{3}}\right)=12\left(3+\dfrac{2}{\sqrt{3}}\right)=36+\dfrac{24}{\sqrt{3}}\\=36+8\sqrt{3}$ cm