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! :)

Printable View

- August 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! :) - August 30th 2006, 10:11 AMThePerfectHackerQuote:

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

- August 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: - August 30th 2006, 10:34 AMThePerfectHackerQuote:

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

(Look at the beautifully artistic picture).

---

You have by the Law of Sines,

From here we have,

Then,

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

- August 30th 2006, 10:38 AMNeffets...:P
Thanks for your answer... ;)

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

You got it right...

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

Quote:

In

How much can you increase , while and 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 whenCode:`B`

*

* *

7 * *

* * 4

* *

* *

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

Then