If P and Q are the triangles of the hypotenuse BC, then Tan ∠ PAQ =?

Let a be AE ⊥ BC, let AC = 1, so CE = root 2 / 2, CQ = root 2 / 3, so EQ = root 2 / 6
Because AE = root 2 / 2, so tan ∠ EAQ = 1 / 3
Substituting the angle doubling formula tan2 α = 2tan α / (1-tan ^ 2 (α))
The results show that Tan ∠ PAQ = 3 / 4

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