Answer:
BC ≈ 9
AC ≈ 15
Step-by-step explanation:
The side adjacent to the given angle is the one whose length is known, so the relevant trig relations are ...
Cos = Adjacent/Hypotenuse ⇒ cos(37°) = AB/AC
Tan = Opposite/Adjacent ⇒ tan(37°) = BC/AB
Then the unknown sides are ...
AC = AB/cos(37°) = 12/cos(37°) ≈ 15
BC = AB·tan(37°) = 12·tan(37°) ≈ 9
__
Additional comment
Rounded to the nearest degree, angles 37° and 53° are the acute angles found in a 3-4-5 right triangle. Since the given side is adjacent to the smallest acute angle (not the hypotenuse), it will correspond to "4" in the 3-4-5 triangle. That means the scale factor is 12/4 = 3, and the other two sides are 3·3 = 9 and 3·5 = 15.
The numbers work out this way only by rounding to tenths or integers.
