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 = ?
Answer & explanation
Correct answer: option 2
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°