Answer:
(1) length AB = 21.0
(2) length BC = 45.0
Step-by-step explanation:
(1) To determine AB, apply Cosine rule;
[tex]|AB|^2 = |AC|^2 + |BC|^2 \ - \ 2[|AC| \times |BC]cos \ C\\\\|AB|^2 = 13^2 + 29^2 \ - \ 2(13 \times 29) cos(41)\\\\|AB|^2 = 1010 - 569.05\\\\|AB|^2 = 440.95\\\\|AB|= \sqrt{ 440.95} \\\\|AB| = 21.0[/tex]
(2) To determine BC, also apply cosine rule;
[tex]|BC|^2 = |AB|^2 + |AC|^2 \ - \ 2[|AB| \times |AC]cos \ A\\\\|BC|^2 = 30^2 + 21^2 \ - \ 2(30 \times 21) cos(123)\\\\|BC|^2 = 1341 - (-686.245)\\\\|BC|^2 = 1341 + 686.245\\\\ |BC| = 2027.245\\\\|BC|= \sqrt{ 2027.245} \\\\|BC| = 45.0[/tex]
