ive been working on my sat's and i cant seem to figure out how to answer the following question.

a right angle is given. the length of ba is 20. what is the approx length of bc?
sin= .643
cos= .766
tan= .839

the answer is 12.9 but i don't know how that is.

I assume bc is the other leg, and ba is one leg.

Isnt Sin of the base angle= bc/ba?

then bc= .643*ba

To answer this question, we can use the trigonometric relationships in a right triangle. We know that the sine of an angle is equal to the ratio of the length of the side opposite that angle to the length of the hypotenuse. In this case, the angle with the right triangle is the base angle.

So, we have:
sin(base angle) = length of bc / length of ba

Since we are given the value of the sine of the base angle as 0.643, we can plug it into the equation:
0.643 = length of bc / 20

Now, we can solve for the length of bc:
length of bc = 0.643 * 20
length of bc ≈ 12.86

The approximate length of bc is 12.86, which rounds to 12.9 as the given answer.