D is a point on the side BC of a triangle ABC such that AD ⊥ BC. E is a point on AD for which AD : ED = 5 : 2. If ∠BAD = 30° and tan(∠ACB) = tan3(∠DBF) then ∠ACB = ?

60° 72° 75° 80°

72°

AE : ED = 5 : 2, BAD = 30° ∴ ∠ABD = 90° - 30° = 60 ∠DBE = \(\frac{60}{(3+2)}×2\) = 24° tan(∠ACB) = tan3(∠DBF) ⇒ ∠ACB = 3 × 24° = 72°