Is the answer D i.e., 16/3 ?

From how I solved it, triangles ABC and ABD are similar due to AA axiom. Hence the sides will be proportional. Try solving it that way. Let me know if you have any doubts or want my solution.

look angle A is 90 degree angle

so

AD^2 = 4^2 + CD^2

and we have another one too ABD

so we have

(3+CD)^2 = 5^2 +AD^2

now substitute AD and you get CD answer

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you can solve it using the above method.

here’s an alternate and quick method (you have to know the formula tho)

tan(D) = cot(B)

4/CD = 3/4

CD = 16/3