Let BC be a.
Let alpha be b.
tanb = 24/a --- (1).
tan(2b) = (24+26)/a
tan(2b) = 50/a
2tanb/(1-tan²b) = 50/a --- (2).
Substituting (1) in (2).
2(24/a)/(1-(24/a)²) = 50/a
(48/a)/((a²-576)/a²) = 50/a
48a/(a²-576) = 50/a
24a/(a²-576) = 25/a
24a² = 25a²-(25*576)
a² = (25*576)
a = 5*24
a = 120 units.
a is the required length, BC.
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