Law of Sines Triangle Problem

[nvidia69]

1. The problem statement, all variables and given/known data
In Triangle ABC, tan A=3/4, tan B=1, and a=10. Find what b equals.


2. Relevant equations
You can use sina/A=sinb/B


3. The attempt at a solution
This problem is really easy using inv tangent functions and what not, but my teacher said we should be able to get it without a calculator.
Doing it with a calculator b will turn out to be 11.8. But if anyone is able to provide a detailed way to get the problem without using a calculator, that would be great.

Thanks

[Mark44]

If tanB = 1, what's the measure of angle B? That's an easy one, and one that you should know. Also, if tanA = 3/4, it's pretty easy to get sinA.

[nvidia69]

well the tanB=1 is equal to 45 degrees, but how can you get sinA from tanA?

[Mark44]

If tanB = 1, then B is 45 degrees - that's what you meant, right?

You have tanA = 3/4. Draw a right triangle and label the side opposite to A as 3 and the side adjacent to A as 4. What does the hypotenuse have to be? From that, what's sinA?