a1234
  • a1234
Are the answers 8 and 10?
Mathematics
jamiebookeater
  • jamiebookeater
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a1234
  • a1234
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anonymous
  • anonymous
I think so.
amistre64
  • amistre64
how do you come to 8 and 10?

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amistre64
  • amistre64
18+9 = 27, not 29
a1234
  • a1234
I thought those are 30-60-90 Triangles, so the hypotenuse would be twice the short side.
a1234
  • a1234
How is the answer 27?
amistre64
  • amistre64
the perimeter is 29 4+5+10+8 = 27, not 29
amistre64
  • amistre64
why would you think its a 30-60-90? nothing indicates to me that that is the case
a1234
  • a1234
Ok...then how do I find AC and AB?
amistre64
  • amistre64
still working on that ... do you ahve options?
a1234
  • a1234
No options
amistre64
  • amistre64
hmm, all i know at the moment is that 10 and 8 dont work out for the stated perimeter. do you agree?
amistre64
  • amistre64
do we know law of sines?
a1234
  • a1234
Yes, 10 and 8 don't work
a1234
  • a1234
But there are no angles for the Law of Sines
amistre64
  • amistre64
im wondering if we can use them in a general sense tho, i havent got a clear approach yet.
amistre64
  • amistre64
other than assuming a 30=60-90 what else are you thinking of?
a1234
  • a1234
I'm wondering if we can use this theorem: An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the two other sides.
amistre64
  • amistre64
sounds reasonable: so the ratio is 5:4, therefore 5k + 4k + 9 = 29 what is k?
a1234
  • a1234
k is 2.2
amistre64
  • amistre64
i was working out something like sin(a')/5 = sin(c)/(ad) sin(a')/4 = sin(b)/(ad) (ad) sin(a') = 5sin(c) (ad) sin(a') = 4sin(b) 5 sin(c) = 4 sin(b) sin(b)/4 = sin(c)/5 = sin(a)/9
amistre64
  • amistre64
20/9 is a more exact number
amistre64
  • amistre64
(5(20)+ 4(20) + 81)/9 (180 + 81)/9 261/9 = 29 of course
a1234
  • a1234
Ok. Thanks!
amistre64
  • amistre64
as long as your thrm is good, that should be it ... me and geometry thrms are not on speaking terms :)

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