Question 1116856
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(1) {{{tan(B) = 4/3}}}  -->  {{{AD/BD = 4/3}}}<br>
(2) {{{cos(C) = 15/17}}}  -->  {{{CD/AC = 15/17}}}<br>
In right triangle ADC, let CD = 15x and AC = 17x; then, using the 8-15-17 Pythagorean Triple, AD = 8x.<br>
With AD = 8x, (1) tells us BD = 6x; then, using the 6-8-10 Pythagorean Triple,  AB = 10x.<br>
We are given that AB=10x is 20cm.  That means AC=17x is 34cm and BC = BD+DC = 6x+15x = 21x is 42 cm.<br>
Answers: AC = 34cm; BC = 42cm.