1) tentukan panjang dan besar sudut yang diketahi dari sgtiga ABC.a) AB=3 , AC=2 akar3 ,sdut C =60 derajat. b)sudut A=120drajat,sudut B=30drjt dan AC=40cm. 2)te

Aturan sinus / cosinus

1. a. ΔABC
AB = 3, AC =2√3, <C = 60

AB/sin C = AC/sin B
sin B = AC. sin C/AB
sin B = 2√3 sin 60 /(3) =(2√3)(1/2√3)/(3)= 1
sin B = 1 = sin 90
<B = 90
<A = 180-90-60= 30

BC/sin A =  AC/sinB
BC = AC. sin A/sin B
BC = 2√3. sin 30 / sin 90
BC = (2√3)(1/2) / (1)
BC = √3

1b.
<A= 120
<B = 30
AC  = 30
<C = 180-120-30 = 30

AB/sin C = AC/sin B
AB = AC. sin C/sin B
AB = (30)(sin 30) /sin (30)
AB = 30


BC /sin A = AC /sin B
BC = AC. sin A/sin B
BC = 30 sin 120/sin 30
BC = (30)(1/2 √3)/(1/2)
BC = 30√3

2. ΔPQR
c. PQ=15 , QR - 10, <R = 30
QR/sin P = PQ/sin R
sin P = QR.sin R/ PQ
sin P = 10(sin 30)/(15)
sin P = 10(1/2)/ (15)= 5/15 = 1/3
cos P = √(1 - sin²P) = √(1 - 1/9) = √(8/9)
cos P = 2/3 √2

d. PQ = 3 , QR = 5,PR = 7
cos P  =  (PQ² + PR² - QR²)/(2.PQ.PR)
cos P =  (9+ 49 - 25)/ (2)(3)(7)
cos P = (33)/(42)
cos P = 11/14