anonymous
  • anonymous
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.)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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ZeHanz
  • ZeHanz
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...
anonymous
  • anonymous
a^2+b^2=c^2. Where do I input 16 and 30?

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anonymous
  • anonymous
16 = a, 30 = c?
ZeHanz
  • ZeHanz
a and b are the rectagular sides, c is the hypothenuse
anonymous
  • anonymous
16^2+b^2=30^2 B= 25.38?
ZeHanz
  • ZeHanz
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.
ZeHanz
  • ZeHanz
So AB=34.
anonymous
  • anonymous
Now what do I do to find CD?
anonymous
  • anonymous
@ZeHanz
ZeHanz
  • ZeHanz
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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