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marcoduuuh Group Title

PLSPLSPLSPLS HELP. In the diagram below, is an altitude of ABD. What is the length of ? If necessary, round your answer to two decimal places. (Picture below.)

  • one year ago
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  1. marcoduuuh Group Title
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    • one year ago
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  2. ZeHanz Group Title
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    First try to prove triangle ACB and ABD are similar. Similar triangles have proportional sides (meaning sides in the big triangle are a constant factor times the sides in the small one). Further hint: you may need the Pythagorean Theorem as well...

    • one year ago
  3. marcoduuuh Group Title
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    a^2+b^2=c^2. Where do I input 16 and 30?

    • one year ago
  4. marcoduuuh Group Title
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    16 = a, 30 = c?

    • one year ago
  5. ZeHanz Group Title
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    a and b are the rectagular sides, c is the hypothenuse

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  6. marcoduuuh Group Title
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    16^2+b^2=30^2 B= 25.38?

    • one year ago
  7. ZeHanz Group Title
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    No, a and b are the rectangular sides. In triangle ACB these are 16 and 30, so c²=16²+30²=256+900=1156, so c=34.

    • one year ago
  8. ZeHanz Group Title
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    So AB=34.

    • one year ago
  9. marcoduuuh Group Title
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    Now what do I do to find CD?

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  10. marcoduuuh Group Title
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    @ZeHanz

    • one year ago
  11. ZeHanz Group Title
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    ACB and ABD are similar, because they both have a right angle, and they have angle A in common. Similar triangles have proportional sides, which means:\[\frac{ AC }{ AB }=\frac{ AB }{ AD }\] (read as: one side in first triangle : same side in other one= same number. Because in the above equation, you know 3 out of four lengths, you can calculate the fourth (AD). Once AD is known, you get CD = AD-16.

    • one year ago
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