anonymous
  • anonymous
Find the missing measures.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1437458115319:dw|
mathstudent55
  • mathstudent55
What do you know about triangles IFE and IHG?
anonymous
  • anonymous
I know that HI=\[3\sqrt{3}\]

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mathstudent55
  • mathstudent55
That is correct, but what about my question?
anonymous
  • anonymous
IFG has 2 side missing and IHG has 1 missing side?
mathstudent55
  • mathstudent55
No, that's not what I mean. Look at the triangles when you separate them. See the figure below. |dw:1437458809533:dw|
nincompoop
  • nincompoop
understand the concept of proportionality or similarity and congruence.
nincompoop
  • nincompoop
if you want, you can solve the smaller portion of right triangle's adjacent side (adjacent to the angle), and then work your way from there
mathstudent55
  • mathstudent55
Now look. Triangle IFE and triangle IHG are both right triangles. That means that each one has a right angle. Right angles are congruent, so you already have one pair of congruent angles.
nincompoop
  • nincompoop
|dw:1437459025019:dw|
mathstudent55
  • mathstudent55
Now also notice that angle I of triangle IFE and angle I of triangle IHG are congruent because they are the same angle. That is a second pair of congruent angles. That makes the triangles similar.
mathstudent55
  • mathstudent55
@nincompoop If instead of writing, you did some more reading, you'd see he already found that out.
mathstudent55
  • mathstudent55
Since we now know we have similar triangles, we use the fact that the corresponding sides have proportional lengths. We set up proportions and find the missing lengths.
mathstudent55
  • mathstudent55
|dw:1437459177765:dw|
mathstudent55
  • mathstudent55
We can use the two sides in black above to establish a ratio of lengths: \(\dfrac{large~triangle}{small~triangle} = \dfrac{5}{3} \)
mathstudent55
  • mathstudent55
|dw:1437459273682:dw|
mathstudent55
  • mathstudent55
\(\dfrac{5}{3} = \dfrac{EG + 6}{6} \) Do you understand this proportion?
nincompoop
  • nincompoop
basic principle: |dw:1437459224575:dw|
nincompoop
  • nincompoop
|dw:1437459427659:dw|
nincompoop
  • nincompoop
|dw:1437459476749:dw|
mathstudent55
  • mathstudent55
\(\dfrac{5}{3} = \dfrac{EG + 6}{6}\) \(6 \times 5 = 3 \times (EG + 6) \) \(30 = 3EG + 18\) \(3 EG = 12\) \(EG = 4\)
triciaal
  • triciaal
|dw:1437459565905:dw|
mathstudent55
  • mathstudent55
|dw:1437459606710:dw|
mathstudent55
  • mathstudent55
We just need to find FH.
mathstudent55
  • mathstudent55
\(\dfrac{6}{3\sqrt 3} = \dfrac{4}{FH} \) \(6FH = 4 \times 3 \sqrt 3\) \(6 FH = 12 \sqrt 3\) \(FH = 2 \sqrt 3\)
nincompoop
  • nincompoop
use tangent ratio
nincompoop
  • nincompoop
page 41 http://www.scribd.com/doc/22374733/Mathematics-Teach-Yourself-Trigonometry
mathstudent55
  • mathstudent55
We can find FH another way. We can solve for FI using the Pythagorean theorem with the large triangle, then subtract HI from it. \((FI)^2 + (FE)^2 = (EI)^2\) \((FI)^2 + 5^2 = 10^2\) \((FI)^2 + 25 = 100\) \((FI)^2 = 75\) \(FI = 5\sqrt3\) \(FH = FI - HI\) \(FH = 5 \sqrt 3 - 3\sqrt 3\) \(FH = 2 \sqrt 3\) As you can see, we get the same result for FH as we did above.
mathstudent55
  • mathstudent55
@SimiYami I hope you can follow my explanations above. If you have any questions, just ask.
nincompoop
  • nincompoop
@triciaal |dw:1437460115571:dw|
anonymous
  • anonymous
I understood what you've explained. Thank you very much for your help again @mathstudent55. Thank you @nincompoop for your example.:)
triciaal
  • triciaal
@nincompoop trig not necessary here I would use pythagorean theorem as shown above even easy to do ratio shown above by @mathstudent55
mathstudent55
  • mathstudent55
@SimiYami You're welcome.
triciaal
  • triciaal
|dw:1437460318944:dw|