anonymous
  • anonymous
Trigonometry help, easy medal and fan
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
the longer leg of a 30-60-90 triangle is 18. what is the length of the other leg
hwyl
  • hwyl
how do you know that this is easy?
hwyl
  • hwyl
there are two ways to solve this problem

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anonymous
  • anonymous
|dw:1443145786138:dw| you can also solve it by trigonometry.
anonymous
  • anonymous
Ey yo thanks!
hwyl
  • hwyl
it says the longer leg, so I am not sure if that pertains to the hypotenuse
hwyl
  • hwyl
longer leg is always across the 60 angle
anonymous
  • anonymous
certainly hypotenuse is longest .
hwyl
  • hwyl
that would be the LONGEST, but the problem says LONGER so we can make it this way long, longer and longest
hwyl
  • hwyl
|dw:1443135576185:dw|
hwyl
  • hwyl
|dw:1443135732498:dw|
hwyl
  • hwyl
\(longleg = y^2 = 2^2 - 1^2 \rightarrow y = \sqrt{3} \)
hwyl
  • hwyl
|dw:1443136114788:dw|
hwyl
  • hwyl
based on these information, without the use of trigonometry, we can use patterns \(shortleg = \frac{1}{2}hypotenuse \)
hwyl
  • hwyl
if shortleg is 1/2 of hypotenuse then \(longleg = shortleg \times \sqrt{3} \)
hwyl
  • hwyl
or \(longleg = \frac{1}{2}hypotenuse \times \sqrt{3} \)
hwyl
  • hwyl
\((18 \times 2) \div \sqrt{3} = hypotenuse \) becase we know that: \(shortleg = \frac{1}{2}~ hypotenuse \)

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