Step-by-step explanation:
the other answer is correct and simple (based on simply applying definitions and formulas).
to help you with understanding the background there are actually 2 direct ways to solve this.
trigonometry is always about angles in a circle. even if and when we are taking about angles in other shapes like triangles. we simply need to imagine a circle around the shape in question going through the important points.
so the first way is to imagine a circle with the center in point C and going through point A.
the radius of that circle is 40 (AC).
so, sin(C) × 40 = 24
cos(C) × 40 = 32
tan(C) = sin(C)/cos(C) = (sin(C)×40)/(cos(C)×40) = 24/32
= 3/4
fit the second way imagine a circle with the center again in point C and going through point B.
the radius of that circle is 32 (BC).
here now tan(C) × 32 = 24 (AB).
yes, AB would in that scenario be directly tan(C), but it is multiplied by the radius.
so, to get the "pure" tan(C), we need to divide this length by the radius.
=> 24 / 32 = 3/4
