Solve tiangle

topsquark

Forum Staff
Jan 2006
11,602
3,457
Wellsville, NY
Ha, ha, ha, I'm professor of math from Serbia. Draw the picture, all is clear.
It's always interesting when the first problem is trying to decipher what the poster is really trying to do. I have attached picture below (not necessarily to scale) of my best guess of what the professor is looking for. I'm guessing the $135^\circ$ may be interior or exterior to the triangle giving an alternate angle $A'$ and corresponding adjacent sides $b'$ and $c'$ to give two triangles.
Here's a picture (click on it to expand):
figure.jpg

@ns1954: Is Walagaster's diagram the one you are using? I don't think we can help you out if we don't have anything more to work with.

-Dan
 
Dec 2009
54
0
Walagaster's draw is Ok, same I used, without point A'. $h_b$ is altitude of triangle, and $\Delta BDC$ is isosceles, right triangle. My native language is serbian, and we use specific termilology for elements of triangle for which I'm not sure I know the english terms. I find this problem in book of probems, and author claims that exist 2 solutions. I see only one.
$\alpha=\arcsin\frac {5}{13}$ and $\beta=\frac {7}{13\sqrt 2}$.
 
Last edited:
Dec 2009
54
0
@DenisB
Your hint leeds also to $b=7$, but with draw it gets easier and faster.
 
Feb 2015
2,255
510
Ottawa Ontario
@DenisB
Your hint leeds also to $b=7$, but with draw it gets easier and faster.
I'll never attend your math classes :)

B


5


D.......5........C........7..............A

BA = 13
Triangle BCD is isosceles...so angle BCA = 135

WHY do you not use Walagaster's point A' ?
Seems to be only way for YOUR 2nd solution.
I pity your poor students :)
 
Dec 2009
54
0
$\gamma=135°$ is given interior angle of triangle, so A' is of no use.
BTW, I'm in retirement, and I was not happy with the students. I feel like a sigh whose song nobody heard. Some like you.
 
Last edited:
Feb 2015
2,255
510
Ottawa Ontario
Ok teacher, here's one for you:

Right triangle 135-352-377 and isosceles triangle 132-366-366
have same area (23760) and same perimeter (864).

Find another similar case which is not a multiple of above.
 

Walagaster

MHF Helper
Apr 2018
230
146
Tempe, AZ
Only someone from Tempe AZ could figure that out :)

Also looks like a 7-24-25 right triangle is involved...right?
Which triangle is that in my picture? I'm not seeing it...