Since m∠B = 90°, then ΔABC is a right triangle, so Pythagorean Theorem can be used to solve for AC.
AB² + BC² = AC²
12² + 16² = AC²
144 + 256 = AC²
400 = AC²
20 = AC
The placement of point K is not given. Is it on AC, inside the triangle, or outside the triangle? In order to find the length, you need to know where it is placed.
Answer: AC = 20, BK = 35/3 ≈ 11.67
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
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