Question

Given: △ABC, m∠B=90°
AB = 12, BC = 16, BK⊥ AC

Find: AC and BK

Answer 1

Answer:AC = 20

BK = 9.6

Step-by-step explanation:

AC is found using the Pythagorean theorem in the usual way:

 AC² = AB² + BC²

 AC² = 12² + 16² = 144 +256 = 400

 AC = √400

 AC = 20

You may recognize this is a 3-4-5 triangle scaled by a factor of 4.

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Then BK is found using similar triangles. All of the triangles in the figure are similar*, so ...

 long side / hypotenuse = BC/AC = BK/AB

 BK = AB(BC/AC) = 12(16/20) = 12×0.8

 BK = 9.6