Diketahui segitiga abc. Panjang sisi ac=b, panjang sisi bc= a cm dan a+b = 10 cm. Jika sudut a = 30 dan sudut b= 60. Tentukan panjang sisi ab

a + b = 10 => a = 10 - b
Aturan sinus
a/(sin A) = b/(sin B)
(10 - b)/(sin 30°) = b/(sin 60°)
(10 - b)/(1/2) = b/(1/2 √3)
(10 - b)/1 = b/√3
b = 10√3 - √3b
b + √3b = 10√3
b(1 + √3) = 10√3
b = 10√3/(1 + √3) . (1 - √3)/(1 - √3)
= 10√3(1 - √3)/(1 - 3)
= 10√3(1 - √3)/-2
= -5√3(1 - √3)
= -5√3 + 15

a = 10 - b = 10 - (-5√3 + 15) = 5√3 - 5

Karena ∆abc siku-siku di C sehingga sisi miringnya sisi AB
AB = √(BC^2 + AC^2)
= √((5√3 - 5)^2 + (-5√3 + 15)^2)
= √(75 - 50√3 + 25 + 75 - 150√3 + 225)
= √(400 - 200√3)
= √(200(2 - √3))
= 20√(2 - √3) cm

= 20√(2 - 2√(3/4))
= 20 √(3/2 + 1/2 - 2√(3/2.1/2))
= 20 (√(3/2) - √(1/2))
= 20 (1/2 √6 - 1/2 √2)
= 10√6 - 10√2
= 10(√6 - √2) cm
= 10√2(√3 - 1) cm