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
1/2 = 6/AC
AC/2 = 6
AC = 6 × 2
AC = 12
The length of AC is 12 cm
PART 2
∠CAD + 30° + 90° = 180°
∠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 = 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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