1. Solve tiangle

Solve triangle in which is

$$b+c=20,\ a=5\sqrt 2,\ \gamma=135°$$

($2$ solutions)

2. Re: Solve tiangle Originally Posted by ns1954 Solve triangle in which is
$$b+c=20,\ a=5\sqrt 2,\ \gamma=135°$$
($2$ solutions)
Normally the word solve is applied to an equation. I don't see any, do you?
So you need to explain and show some effort. This is not a homework service.

3. Re: Solve tiangle

u = alpha, v = beta, w = gamma
w = 135, v = 180 - 135 - u = 45 - u

5sqrt(2) / SIN(u) = (20-b) / SIN(135) = b / SIN(45 - u)

Above is a hint.
Sorry, homework not done here...

Not sure what you're solving for...so solve for whatever turns you on!!

4. Re: Solve tiangle

Solve triangle means find basic elements of triangle
$$a,\ b,\ c,\ \alpha,\ \beta,\ \gamma.$$
I have solutions which demand picture which I don't know how to draw. And, please somebody to tell me where to post problems like challenges.

If $D-C-A,\ and\ BD=h_b$ then $BD=DC=5$ and from $\Delta ABD$ with Pithagoras law we have

$$(20-b)^2=5^2+(b+5)^2$$

which gives $b=7$. Te rest is easy, but this give me just one solution.

5. Re: Solve tiangle Originally Posted by ns1954 Solve triangle means find basic elements of triangle
$$a,\ b,\ c,\ \alpha,\ \beta,\ \gamma.$$
I have solutions which demand picture which I don't know how to draw. And, please somebody to tell me where to post problems like challenges.

If $D-C-A,\ and\ BD=h_b$ then $BD=DC=5$ and from $\Delta ABD$ with Pithagoras law we have

$$(20-b)^2=5^2+(b+5)^2$$

which gives $b=7$. Te rest is easy, but this give me just one solution.
No idea what you're doing...
You gave one of the angles as 135: so IMPOSSIBLE for triangle to be a right triangle...

Are you a student attending math classes?

6. Re: Solve tiangle

Ha, ha, ha, I'm professor of math from Serbia. Draw the picture, all is clear.

7. Re: Solve tiangle Originally Posted by ns1954 If $D-C-A,\ and\ BD=h_b$
What the hell does that mean????

Can you at least describe what the diagram would look like?

8. Re: Solve tiangle Originally Posted by DenisB What the hell does that mean????
Can you at least describe what the diagram would look like?
Denis, $D-C-A$ is standard notation is axiomatic geometry. It means that $D,~C,~\&~A$ are colinear points and $C$ is between $D~\&~A$.
But I'll be damn if I know what this professor troll means by it.

9. Re: Solve tiangle

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):

10. Re: Solve tiangle

Only someone from Tempe AZ could figure that out Also looks like a 7-24-25 right triangle is involved...right?

11. Re: Solve tiangle Originally Posted by ns1954 Ha, ha, ha, I'm professor of math from Serbia. Draw the picture, all is clear. Originally Posted by Walagaster 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): @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

12. Re: Solve tiangle

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 $\beta=\frac {7}{13\sqrt 2}$.

13. Re: Solve tiangle

@DenisB
Your hint leeds also to $b=7$, but with draw it gets easier and faster.

14. Re: Solve tiangle Originally Posted by ns1954 @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 15. Re: Solve tiangle

$\gamma=135°$ 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.