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## #1 2006-01-21 04:53:08

katy
Member
Registered: 2005-12-28
Posts: 14

### I need help with this problem please!!

Hi...I have a problem that really needs to be solved for my study for the exam please.(it is grade 11 problem.)

1) a) If <C=40degrees, c=35 and b=40 in triangle ABC, then determine the number of triangles that would be possible with these values. Justify your answer by showing your work.

Many thanks to you guys..!!:P;)

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## #2 2006-01-21 05:24:11

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: I need help with this problem please!!

I am a little lost.  If everything you typed in a) is what you wished type then there is only one triangle possible.  Unless there is an equal sign somewhere that shouldn't be there;

A+B+C = 180°

Using the law of sines;

sin40°/35 = sinB/40

B = arcsin(40sin40°/35) ≈ 47.2746°

If C = 40° and B ≈ 47.2746°, then A ≈ 92.7254°

A = 92.7254°,  a = 54.388
B = 47.2746°,  b = 40
C = 40°,          c = 35

Nothing else is possible unless C, c, or b are allowed to vary.

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## #3 2006-01-21 06:21:25

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: I need help with this problem please!!

There is a second possible triangle.

B can also take the value of (180 - 47.2746)°.

Why did the vector cross the road?
It wanted to be normal.

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## #4 2006-01-21 07:21:17

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: I need help with this problem please!!

Good catch Mathsyperson,  I should not rely so heavily on the law of sines.  Perhaps an expansion of the law of cosines would be more appropriate?  I am wondering if the radical sign would produce two simultaneous solutions like we needed here.

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## #5 2006-01-21 08:07:34

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: I need help with this problem please!!

The law of cosines would give this:

35² = 40² + a² - 2*40*a cos 40°.

Rearranging gives a² - 80 cos40° a - 375 = 0, which is a quadratic that can be solved to give the two possible lengths of the third side.

I think the sine law would be simpler to use, you just need to remember to work out all possible values of the arcsin. It's not you relying on the law of sines that's the problem, it's you relying on your calculator.

Sorry, but what's the radical sign?

Why did the vector cross the road?
It wanted to be normal.

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## #6 2006-01-21 08:49:27

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: I need help with this problem please!!

C = √(A² + B² - 2ABcosc)

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## #7 2006-01-21 09:06:34

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: I need help with this problem please!!

Oh, of course. Sorry, it's just that I don't hear 'radical' being used to mean square root very often, so I forgot about that definition temporarily.

Why did the vector cross the road?
It wanted to be normal.

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## #8 2006-01-21 11:21:00

Member
Registered: 2006-01-21
Posts: 1

### Re: I need help with this problem please!!

how do you solve x - the square root of x = 0 i really need some help with this one.

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## #9 2006-01-21 11:37:51

irspow
Member
Registered: 2005-11-24
Posts: 457

x - √x = 0

x = √x

x² = x

x = 1

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## #10 2006-01-21 11:58:12

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: I need help with this problem please!!

...or 0.

Why did the vector cross the road?
It wanted to be normal.

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## #11 2006-01-21 12:07:34

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: I need help with this problem please!!

aaaaargh!....yes.

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## #12 2006-01-21 19:23:40

kempos
Member
Registered: 2006-01-07
Posts: 77

x^2=x
x^2-x=0
x(x-1)=0
x=1 v x=0

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