Question

Triunghiul dreptunghic ABC cu m(BAC)=90 grade si m(ABC)=30 grade are BC=16 cm. Latura patratului AMPQ unde M∈(AC), P∈(BC), Q∈(AB) este de: a) 8 cm b) 4(3-√3) cm c) 4 cm d) 4(3+√3) cm

Answer 1

sin 30⁰=AC/BC
1/2=AC/16
AC=16/2
AC=8 cm
cos 30⁰=AB/BC
√3/2=AB/16
AB=16√3/2
AB=8√3 cm

BQ/AB =PQ/AC  notal AQ=PQ=x
(8√3-x)/8√3=x/8
(8√3-x)/√3=x
8√3-x=x√3
x√3+x=8√3
x(√3+1)=8√3
x=8√3/(√3+1)=8√3(√3-1)/(3-1)=(24-8√3)/2=12-4√3=4(3-√3) cm
raspuns corect b)