Question

Tentukan besar sudut c jika diketahui sudut a = 60 derajat, sisi a = 5 cm Dan sisi b = 5√6/3 cm !

Answer 1

A/sin A = b/sin B
sin B = b. sin A/ a
sin B = (5/3 √6)(1/2 √3) / (5)
sin B = (5/3 x 1/2) x√6 x √3 / (5)
sin B =   (5/6)√18  / (5)
sin B =  (5/6 : 5) √18 = (1/6)(3√2) = (3/6) √2 = 1/2√2
sin B = 1/2 √2 = sin 45
∠B = 45°
∠C = ∠(180 - A - B)
∠C = 75°
c/sin C = a/sin A
c = a. sin C/sin A
c= 5  sin 75/ sin 60
c = 5(1/4 (√6 + √2)) / (1/2 √3)
c =  (5/2)(√6 + √2) / √3
c = (5/6)(√3)(√6+√2)
c = 5/6 (√18 + √6)
c = 5/6 (3√2 + √6)