My Math Forum Finding The Length Of AB

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March 9th, 2017, 02:38 PM   #1
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Finding The Length Of AB

I'm currently having trouble with this question, my teacher has given me.

Find in triangle ABC, sinA=0.5, sinB=0.7, a=9, Find the length of AB.

The triangle looks like the one present.

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Last edited by TotalMathMan; March 9th, 2017 at 03:19 PM.

 March 9th, 2017, 03:08 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,849 Thanks: 957 SinC cannot equal 9 you're going to need the length of at least one side. that triangle can be grown or shrunk as much as you like and still keep those angles. Check the problem again.
 March 9th, 2017, 03:11 PM #3 Senior Member   Joined: Aug 2012 Posts: 1,850 Thanks: 508 I think that's a trick question. Do you know about similar triangles? There's a triangle with those same angles for any length you can name. 10 miles, a million miles, an inch. Did you leave out any info? Or does your teacher like to play tricks?
March 9th, 2017, 03:16 PM   #4
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Quote:
 Originally Posted by romsek SinC cannot equal 9 you're going to need the length of at least one side. that triangle can be grown or shrunk as much as you like and still keep those angles. Check the problem again.
I went ahead and adjust it I believe I might have read it wrong, thank you for pointing that out.

March 9th, 2017, 03:18 PM   #5
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Quote:
 Originally Posted by Maschke I think that's a trick question. Do you know about similar triangles? There's a triangle with those same angles for any length you can name. 10 miles, a million miles, an inch. Did you leave out any info? Or does your teacher like to play tricks?
I doubt it, worse case scenario I can go ahead and ask for help tomorrow from her.

 March 9th, 2017, 04:50 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,841 Thanks: 1564 Which of the triangle's angles is obtuse?
March 9th, 2017, 06:06 PM   #7
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Quote:
 Originally Posted by TotalMathMan Thanks for the quick reply! I went ahead and adjust it I believe I might have read it wrong, thank you for pointing that out.
Just use the law of sines; it's a one line calculation.

Last edited by skipjack; March 10th, 2017 at 03:08 AM.

 March 10th, 2017, 03:09 AM #8 Global Moderator   Joined: Dec 2006 Posts: 18,841 Thanks: 1564 It's not quite that simple, as the angle opposite AB isn't given.
March 10th, 2017, 06:19 AM   #9
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Quote:
 Originally Posted by romsek Just use the law of sines; it's a one line calculation.
ok, not quite one line.

Law of sines

$\dfrac{\sin(A)}{a} = \dfrac{\sin(B)}{b}$

$\dfrac{0.5}{9} = \dfrac{0.7}{b}$

$b = 12.6$

$\sin(C) = \sin( \pi - \arcsin(0.5) - \arcsin(0.7) ) \approx 0.963$

$\dfrac{\sin(C)}{c} = \dfrac{\sin(A)}{a}$

$c \approx 17.34$

 March 10th, 2017, 08:11 AM #10 Global Moderator   Joined: Dec 2006 Posts: 18,841 Thanks: 1564 Why did you calculate the value of b, but then not use it to find c?

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