# Solve tiangle

#### ns1954

Solve triangle in which is

$$b+c=20,\ a=5\sqrt 2,\ \gamma=135°$$

($2$ solutions)

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#### Plato

MHF Helper
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.

1 person

#### DenisB

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!!

#### 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.

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#### DenisB

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?

#### ns1954

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

#### DenisB

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?

#### Plato

MHF Helper
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.

2 people

#### Walagaster

MHF Helper
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):

#### Attachments

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1 person

#### DenisB

Only someone from Tempe AZ could figure that out

Also looks like a 7-24-25 right triangle is involved...right?

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