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Provided that A and B are acute angles and sin A = sin B, prove that A = B

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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,101

Draw right triangles ABC and PQR.

Prove that B = Q

We know that Sin B = Sin Q so:

We can manipulate the above to

b / q = c / r = k

b = kq and c = kr

Pull the k^2 out to simplify.

So

ΔABC is similar to ΔPQR

B = Q

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**{7/3}****Member**- Registered: 2013-02-11
- Posts: 210

Sin A=a/c and sin B=b/c then a=b ,so in two right triangles with angle A and B ,oposite side is a=b,hypottenuse is c,other side must be equal.thus two triangles are congruent,A=B

*Last edited by {7/3} (2013-06-29 16:49:10)*

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Thanks

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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{7/3} wrote:

Sin A=a/c and sin B=b/c then a=b ,so in two right triangles with angle A and B ,oposite side is a=b,hypottenuse is c,other side must be equal.thus two triangles are congruent,A=B

But the two right triangles are not congruent! You certainly cannot say that two right triangles containing equal angles are congruent.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,182

They both have a side 'c'.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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What if they do not have?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**zetafunc.****Guest**

Are you required to give a geometric proof?

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,182

Agnishom wrote:

What if they do not have?

Start with two right angled triangles, both with hypotenuse c. Let one have angle A and the other B.

Use the equal sines property to show that a = b. Then they are congruent.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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In that case are we not assuming that A + B = 90degree ?

zetafunc wrote:

Are you required to give a geometric proof?

Well, yeah. But I would love to see any other proofs you have

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,101

I thought that you would have found post #2 particularly relevant.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,182

hi Agnishom,

Let's start again, shall we. Draw a right angled triangle with angle A, hypotenuse c, opposite a. Draw another with hypotenuse c and opposite B. See diagram below.

From the first sinA = a/c

from the second sinB = b/c

But sinA = sinB , therefore a/c = b/c , therefore a = b

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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