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AB = 4
<C = 30
AC/sin B = AB/sin C
sin B = AC/AB . sin C
sin B = (4√2)/(4) . sin 30
sin B =¹/₂ √2 -> B = 45
<A= 180 - <B- <C = 180 - 30 - 45
<A = 105
2. PR = 10, PQ = 12, <P = 120
QR² = PR² + PQ² - 2(PR)(PQ) cos P
QR² = 100 + 144 -2(10)(12)(-1/2)
QR² = 244 + 120
QR² =364--> QR = 2√91
3. PQ =QR = 25, PR= 20
cos <Q = (PQ²+QR² - PR²) / (2)(PQ)(QR)
cos <Q = (625 +625 - 400) / (2)(25)(25) = 850/1.250 = 17/25
<Q = cos⁻¹( 17/25) = 47,2