Question

Look at the figure:

Answer 1

If tan(x) = a/4, then a is opposite to the angle x and 4 is adjacent to the angle x

If cos(x) = 4/b, then 4 is adjacent to the angle x and b is the hypotenuse

sin(x) =  opposite/hypotenuse = a/b

Answer is D.

Answer 2

ANSWER

$\sin(x) = \frac{a}{b}$


EXPLANATION

It was given that,

$\tan(x) = \frac{a}{4}$



and

$\cos(x) = \frac{4}{b}$


We can use the relation,

$\tan(x) = \frac{ \sin(x) }{ \cos(x) }$


This implies that,


$\cos(x) \times \tan(x) = \sin(x)$





We now substitute the given values to get,


$\frac{a}{4} \times \frac{4}{b} = \sin(x)$

$\sin(x) = \frac{a}{b}$


Or

Since

$\tan(x) = \frac{a}{4} = \frac{opposite}{adjacent}$


It means the length of the opposite side is
$a \: units$


and the length of the adjacent side is
$4 \: units$


Also,

$\cos(x) = \frac{4}{b} = \frac{adjacent}{hypotenuse}$


This also means that, the hypotenuse is
$b \: units$



But
$\sin(x) = \frac{opposite}{hypotenuse}$


This implies that,


$\sin(x) = \frac{a}{b}$


The correct answer is D.