Diketahui Segitiga mempunyai panjang sisi

AC = b meter
BC = a meter a + b = 12 meter
Jika
Sudut A = 60°
Sudut B = 30°

maka panjang sisi AB = …….. meter

Diketahui Segitiga mempunyai panjang sisi

Jawaban Terkonfirmasi

A+b = 12
a = 12 – b
c = 180 – 60- 30
= 90
aturan sinus pada segitiga
$$begin{align} frac{a}{sin 60} &= frac{b}{sin 30}\ frac{12-b}{ frac{1}{2} sqrt{3} }&= frac{b}{ frac{1}{2} }\ frac{1}{2} sqrt{3} b &= 6 - frac{1}{2}b\ frac{ sqrt{3} }{2} b &= 6 - frac{1}{2}b \ frac{ sqrt{3} }{2} b - frac{1}{2}b &= 6 \ frac{ sqrt{3}-2 }{2} b &= 6 \ b &= 6times frac{ sqrt{3}-2 }{2}\ b &= 3times sqrt{3}-2 \ end{align}$

AB = sisi c
$$begin{align} frac{c}{sin 90} &= frac{b}{sin b}\ frac{c}{1}&= frac{3 sqrt{3}-6}{ frac{1}{2} } \ frac{1}{2}c &= 3 sqrt{3}-6 \ c &= 3 sqrt{3}-6 times 2\ c &= 6 sqrt{3}- 12 end{align}$

Jawaban Terkonfirmasi

a + b = 12 ⇔ a = 12 – b

Aturan Sinus
$Rightarrow frac{ alpha }{sin 60^o} = frac{b}{sin 30^o} \ \ Leftrightarrow frac{ 12 - b }{ _{frac{1}{2} sqrt{3}} } = frac{b}{_ { frac{1}{2} }} \ \ Leftrightarrow 12 - b = b sqrt{3} Rightarrow b Rightarrow frac{12}{_{ sqrt{3} +1 }} \ \$

$Rightarrow frac{AB}{sin 90^o} = frac{b}{sin 30^o} \ \ Leftrightarrow AB = ( frac{12}{_{ sqrt{3} +1}} ) star frac{1}{_{ frac{1}{2} }} = frac{24}{ _{sqrt{3} +1}} \ \ Leftrightarrow AB = ( frac{24}{_{ sqrt{3} +1}} ) star frac{ sqrt{3}-1 }{_{sqrt{3}-1}} = frac{24( sqrt{3}-1 )}{ _{3-1}} = frac{24( sqrt{3}-1)}{2} \ \ Leftrightarrow AB = 12 sqrt{3} - 12$