Answer:
The value of BD is 6√3 cm and BF = 3√3 cm.
Explanation:
Firstly, we have to find the length of BD using Tangent Rule, tanθ = oppo./adj. :
θ = 60°
adj. = 6 cm
oppo. = BD
tan 60° = BD/6
BD = 6 tan 60°
= 6√3 cm
Next, we have to find the length of BF but we have to find the angle of BAF first. In order to find the angle of BAF, we have to substract ∠ACE and ∠AEC from 180° as the total interior angle for triangle is 180° :
∠CAE + ∠ACE + ∠AEC = 180°
∠CAE + 60° + 90° = 180°
∠CAE = 180° - 90° - 60°
= 30°
∠BAF = ∠CAE = 30°
θ = 30°
oppo. = BF
adj. = 9 cm
tan 30° = BF/9
BF = 9 tan 30°
= 3√3 cm