In triangle ABC, angle C is 90 °, cosA = 5/13, BC = 12. find AB.

univerkov | August 2, 2021 | education

Let’s designate the sides of our triangle as BC = a = 12, AB = c, AC = b.
Cos A = b / c = 5/13
a = 12
a2 + b2 = c2, compose and solve the equation
b = 5 * c / 13
122 + (5 * c / 13) 2 = c2
144 + 25c2 / 169 = c2
25c2 + 144 * 169 = 169c2
144c2 = 144 * 169
c2 = 169
c = 13
Answer: AB = c = 13

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