Hi...

In a triangle ABC are AB= 7 cm, BC= 4cm and angle BAC = 32 degrees...

How much can you increase angle BAC, while AB and BC are unchanged?

Can you guys help me on this?

Would be appreciated! :)

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- Aug 30th 2006, 09:46 AMNeffets...:PHow much?
Hi...

In a triangle ABC are AB= 7 cm, BC= 4cm and angle BAC = 32 degrees...

How much can you increase angle BAC, while AB and BC are unchanged?

Can you guys help me on this?

Would be appreciated! :) - Aug 30th 2006, 10:11 AMThePerfectHackerQuote:

Originally Posted by**Neffets...:P**

- Aug 30th 2006, 10:18 AMNeffets...:P...
No, I'm not trying to find the opposite side...

Kinda hard to explain this... How large can the angle BAC be if AB and BC have the length i wrote before? In other words increase the angle BAC to the point where CB "falls" off AC. Understand?

:confused: - Aug 30th 2006, 10:34 AMThePerfectHackerQuote:

Originally Posted by**Neffets...:P**

(Look at the beautifully artistic picture).

---

You have by the Law of Sines,

$\displaystyle \frac{\sin 32^o}{4}=\frac{\sin C}{7}$

From here we have,

$\displaystyle \sin C=\frac{7}{4}\sin 32^o\approx .9274$

Then,

$\displaystyle C\approx 68.0268^o$

But that is not the only answer. There is one more in the second quadrant namely,

$\displaystyle 180^o-C\approx 111.9732^o$ - Aug 30th 2006, 10:38 AMNeffets...:P
Thanks for your answer... ;)

- Aug 30th 2006, 10:46 AMCaptainBlackQuote:

Originally Posted by**Neffets...:P**

triangle with AB=7 and BC=4cm, and all such triangles occur for some

position of C on this circle.

The largest value of angle BAC occurs when AC is a tangent to this

circle, and angle ACB is a right angle. Then sin(BAC)=4/7, or the maximum

angle BAC=34.85 degrees. (You might want to try to prove this)

RonL

RonL - Aug 30th 2006, 10:50 AMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

32 degrees. What is the largest size of this angle for a triangle with AB and

BC maintaining the given values.

RonL - Aug 31st 2006, 08:04 AMNeffets...:P..
Thats right Captain!

You got it right...

Thanks for all of your help :D - Aug 31st 2006, 01:47 PMSoroban
Hello, Neffets!

Quote:

In $\displaystyle \Delta ABC,\;AB= 7\text{ cm, }BC= 4\text{ cm and }\angle A = 32^o$

How much can you increase $\displaystyle \angle A$, while $\displaystyle AB$ and $\displaystyle BC$ are unchanged?

From the given information, there are two possible triangles.Code:`B B`

* *

* * * *

7 * * 7 * *

* * 4 * * 4

* * * *

* 32° * * 32° *

A * * * * * * * C A * * * * * * * * * * * * * C

The limit is when $\displaystyle C = 90^o.$Code:`B`

*

* *

7 * *

* * 4

* *

* *

A * * * * * * * * * * C

Then $\displaystyle A \:=\:\sin^{-1}\left(\frac{4}{7}\right) \:\approx\:34.85^o$