Answer:
Missing length = 20
Step-by-step explanation:
Ratio is 16/20=4/5
25×4/5=20
We write an inequality:



This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination.

is a linear function while

is an exponential one (with limit zero as

approaches

). We see that

at approximately

and

.
Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at

. By observing our graph, we see that

when

or

.
Since you need a little bit of trigonometry to solve this problem,
I'm pretty sure you've had a little bit of trigonometry in class before
you were assigned to solve this problem.
-- The shaded triangle comes from taking the equilateral triangle and
either folding it in half or cutting it in half.
-- The base that the new triangle is standing on is 1/2 the base of the
equilateral triangle, so it's 7 cm long.
-- The acute angle at the right end of the base is the same as it was in
the equilateral triangle . . . 60 degrees.
-- The tangent of 60 degrees is (opposite side)/(adjacent side) = x / 7 cm
tan(60) = x/7
-- Multiply each side of this little equation by 7 : 7 tan(60) = x
If you don't have the tangent of 60 degrees in your pocket, you can
find it with your calculator. Multiply it by 7, and Shazam, you know 'x' .