Need quick! given triangle abc, which equation could be used to find the measure of angle b?
plz look at pic for answers

second option

Step-by-step explanation:

We are going to use the acronym:

"Soh Cah Toa".

Why? It tells us the right-triangle definitions of sine, cosine, and tangent.

sine is opposite over hypotenuse.

cosine is adjacent over hypotenuse.

tangent is opposite over adjacent.

So looking at our triangle with respect to B tells us that 3 is the opposite measurement and 6 is the adjacent.  No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by .

So let's look at cos(B).

We need to rationalize the denominator by multiplying top and bottom by sqrt(5):

So now looking at sin(B).

We have to rationalize again by multiplying top and bottom by sqrt(5):

.

So looking at our triangle with respect to A tells us that 3 is the adjacent measurement and 6 is the opposite.  No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by .

We don't have to use any trigonometric ratios with A.

12cm

the answer is d