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!

Results 1 to 9 of 9

- Aug 30th 2006, 10:46 AM #1

- Joined
- Aug 2006
- Posts
- 12

- Aug 30th 2006, 11:11 AM #2

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Aug 30th 2006, 11:18 AM #3

- Joined
- Aug 2006
- Posts
- 12

- Aug 30th 2006, 11:34 AM #4

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

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,

- Aug 30th 2006, 11:38 AM #5

- Joined
- Aug 2006
- Posts
- 12

- Aug 30th 2006, 11:46 AM #6

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 5

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, 11:50 AM #7

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 5

- Aug 31st 2006, 09:04 AM #8

- Joined
- Aug 2006
- Posts
- 12

- Aug 31st 2006, 02:47 PM #9

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 846

Hello, Neffets!

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