-
D is a point on the side BC of a triangle ABC such that AD ⊥BC. E is a point on AD for which AE : ED = 5 : 1. If ∠BAD = 30° and tan (∠ ACB) = 6 tan (∠DBE), then ∠ACB =
-
- 30°
- 45°
- 60°
- 15°
- 30°
Correct Option: C
According to question , we draw a figure of a triangle ABC
Given , ∠ BAD = 30° , AE : ED = 5 : 1 and tan (∠ ACB) = 6 tan (∠DBE)
∠ ABD = 60° [∵ ∠ADB = 90°]
| = | |||
| tan ∠DBE | DE/BD |
| = | × | = 6 | |||
| DC | DE | DC |
| ∴ 6 | = 6 | |
| DC |
⇒ BD = DC
∆ ADB ≌ ∆ ADC
⇒ ∠ABD = ∠ACD = 60°
∴∠ ACB = 60°
Hence, ∆ ABC is an equilateral triangle
