In triangle ABC,∠B=90∘ Point X is on ¯AC such that ∠BXA=90∘,AX=12 and CX=4. What is BX?
Triangle ABC is a right triangle, so by the Pythagorean Theorem, AC=122+42=13. Then by the Pythagorean Theorem in triangle ABX, BX^2 = 12^2 - 4^2 = 144 - 16 = 128, so BX= sqrt(128) = 8*sqrt(2).
+9 
