geometry

Given: ΔАВС, m∠ACB = 90°
CD⊥AB
, m∠ACD = 30°
AC = 6 cm.
Find: BD

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  1. PART 1
    Use ratio of sin to find AC
    sin of an angle = side in front of the angle / hypotenuse
    Look at ΔACD
    cos of an angle = side in front of the angle / hypotenuse
    cos 30° = AD/AC
    1/2 = 6/AC
    AC/2 = 6
    AC = 6 × 2
    AC = 12
    The length of AC is 12 cm
    PART 2
    Find the measure of ∠CAD
    ∠CAD + ∠ACD + ∠ADC = 180°
    ∠CAD + 30° + 90° = 180°
    ∠CAD + 120° = 180°
    ∠CAD = 180° - 120°
    ∠CAD = 60°
    ∠CAB = ∠CAD
    ∠CAB = 60°

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  2. Here is the rest:
    PART 3Use ratio of cos to find ABcos of an angle = side adjacent to the angle / hypotenuse
    Look at ΔABCcos of an angle = side adjacent to the angle / hypotenusecos ∠CAB = AC/ABcos 60° = 12/AB1/2 = 12/ABAB/2 = 12AB = 12 × 2AB = 24The length of AB is 24 cm
    PART 4
    Find BD
    BD = AB - AD
    BD = 24 - 6
    BD = 18
    The length of BD is 18 cm

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  3. Hope this helps.

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  4. It should be easy to see that you have 3 similar triangles of
    the form 30-60-90° which have sides in the ratio 1 : √3 : 2
    in ΔACD , CD/AC = √3/2
    CD/6 = √3/2
    CD = 3√3

    in ΔBDC, BD/CD = √3/1
    BD/3√3 = √3/1
    BD = 9

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  5. How did you get that?

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  6. Yu are all wong the rght anser is 15 because 1 + 3= 6

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