Answer:
C) 12/9 = 4/3
Explanation:
it is a right-angled triangle.
Pythagoras applies.
cos(theta) = 9/15
that is the horizontal leg in relation to the baseline (Hypotenuse).
since we are only dealing with ratios here, to get the vertical leg and its relation to the Hypotenuse, we can simply use the numbers of the ratio.
15² = vleg² + 9²
225 = vleg² + 81
vleg² = 144
vleg = 12
therefore,
sin(theta) = 12/15
tan(theta) = sin(theta)/cos(theta) = 12/15 / 9/15 = 12/9 = 4/3
FYI : to prove to you how irrelevant the absolute lengths in ratios are, here a variation with simplified fractions or ratios :
cos(theta) = 9/15 = 3/5
5² = vleg² + 3²
25 = vleg² + 9
vleg² = 16
vleg = 4
therefore,
sin(theta) = 4/5
tan(theta) = sin(theta)/cos(theta) = 4/5 / 3/5 = 4/3
as you see, all as above.
for these kind of calculations we only need ratios (or relative sizes)