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3 years ago

I need help 20 points

Mathematics

1 answer:

forsale [732]3 years ago

3 0

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

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$\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,$

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