3 angles

[iren.perch]

See attached file.
Can someone help me?
I know that alpha= 45 degrees and that a+b+y is maximum 90 degrees, but nothing more actually...

 

[Steven G]

What is the tan(b)? So what is b?
What is the tan(y)? So what is y?

How did you conclude that a+b+y is at most 90??

 

[lookagain]

Stating that the sum of the three angles [has a maximum of] 90 degrees means
that their sum is not greater than 90 degrees. This means you can eliminate
the last two answer choices from that information alone, if you were able to show
that that is the case.

 

[MarkFL]

Hello, and welcome to FMH!

We can see that:

[MATH]\beta=\arctan\left(\frac{1}{2}\right)[/MATH]
[MATH]\gamma=\arctan\left(\frac{1}{3}\right)[/MATH]
Hence:

[MATH]\tan(\beta+\gamma)=\frac{\dfrac{1}{2}+\dfrac{1}{3}}{1-\dfrac{1}{2}\cdot\dfrac{1}{3}}=?[/MATH]

 

[iren.perch]

What is the tan(b)? So what is b?
What is the tan(y)? So what is y?

How did you conclude that a+b+y is at most 90??

Sorry I forgot to state that I'm not allowed to use a calculator

 

[iren.perch]

Hello, and welcome to FMH!

We can see that:

[MATH]\beta=\arctan\left(\frac{1}{2}\right)[/MATH]
[MATH]\gamma=\arctan\left(\frac{1}{3}\right)[/MATH]
Hence:

[MATH]\tan(\beta+\gamma)=\frac{\dfrac{1}{2}+\dfrac{1}{3}}{1-\dfrac{1}{2}\cdot\dfrac{1}{3}}=?[/MATH]

=1 => b + y=45 => answer is C Thank you!