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marcoduuuh

  • one year ago

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.)

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  1. marcoduuuh
    • one year ago
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  2. ZeHanz
    • one year ago
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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...

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

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

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

  6. marcoduuuh
    • one year ago
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    16^2+b^2=30^2 B= 25.38?

  7. ZeHanz
    • one year ago
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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.

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

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

  10. marcoduuuh
    • one year ago
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    @ZeHanz

  11. ZeHanz
    • one year ago
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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.

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