In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.

Accepted Solution

Answer:The answer is 6 inchesStep-by-step explanation:Since the angle is isosceles, angle A and angle B have the same measure, The sum of the angles of any triangle is 180°.So 2 times the measure of angle B plus  120° = 180°, then the equation:
Solving for x we get: Now we use the law of sine on the triangle BMC like this:
Solving for BC we get : We apply the law of sin again on the isosceles triangle ABC like this:
Solving for AB we get:6 inches