A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Find the missing measures.
anonymous
 one year ago
Find the missing measures.

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437458115319:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3What do you know about triangles IFE and IHG?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know that HI=\[3\sqrt{3}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3That is correct, but what about my question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0IFG has 2 side missing and IHG has 1 missing side?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3No, that's not what I mean. Look at the triangles when you separate them. See the figure below. dw:1437458809533:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0understand the concept of proportionality or similarity and congruence.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0if 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
 one year ago
Best ResponseYou've already chosen the best response.3Now 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
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437459025019:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Now 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
 one year ago
Best ResponseYou've already chosen the best response.3@nincompoop If instead of writing, you did some more reading, you'd see he already found that out.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Since 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
 one year ago
Best ResponseYou've already chosen the best response.3dw:1437459177765:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3We can use the two sides in black above to establish a ratio of lengths: \(\dfrac{large~triangle}{small~triangle} = \dfrac{5}{3} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3dw:1437459273682:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\dfrac{5}{3} = \dfrac{EG + 6}{6} \) Do you understand this proportion?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0basic principle: dw:1437459224575:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437459427659:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437459476749:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\dfrac{5}{3} = \dfrac{EG + 6}{6}\) \(6 \times 5 = 3 \times (EG + 6) \) \(30 = 3EG + 18\) \(3 EG = 12\) \(EG = 4\)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437459565905:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3dw:1437459606710:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3We just need to find FH.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\dfrac{6}{3\sqrt 3} = \dfrac{4}{FH} \) \(6FH = 4 \times 3 \sqrt 3\) \(6 FH = 12 \sqrt 3\) \(FH = 2 \sqrt 3\)

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0page 41 http://www.scribd.com/doc/22374733/MathematicsTeachYourselfTrigonometry

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3We 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
 one year ago
Best ResponseYou've already chosen the best response.3@SimiYami I hope you can follow my explanations above. If you have any questions, just ask.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0@triciaal dw:1437460115571:dw