Question 816261
<pre>
One way is:
For very thin right triangles, the adjacent side and the hypotenuse
are very nearly the same, so the opposite/hypotenuse is very close to
the opposite/adjacent.

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To elaborate on the other tutor's answer,

{{{sin(theta)/cos(theta)}}} = {{{tan(theta)}}}

Multiply both sides by {{{cos(theta)}}}

{{{sin(theta)}}} = {{{tan(theta)cos(theta)}}}

Divide both sides by {{{tan(theta)}}}


{{{sin(theta)/tan(theta)}}} = {{{cos(theta)}}}

When {{{theta}}} is very near to zero, the right side {{{cos(theta)}}} is 
very near to 1, since {{{cos(0)}}} = 1

so the ratio of the sine to the tangent is very near to 1, which means
they are nearly equal.

Edwin</pre>