Question 210922
Okay, here we go:

{{{h=d/(cota + cotb)}}}

COT is simply the opposite of TAN, correct? this means that: TAN=opp/adj; COT=adj/opp

So;
(A) Using the figure, show that {{{h=d/(cot a + cot b)}}}
_____/|\
____/_|__\
___/__|____\
__/___|h_____\
_/____|________\
/_a)__|]_______(b_\
__{{{(x)}}}__|___{{{(d-x)}}}
|--------- {{{d}}} ---------|
Notice that we split {{{d}}} between the two triangles with {{{x}}} and {{{d-x}}} That is where we will begin
We start by recognizing that;
cota={{{x/h}}}
cotb={{{(d-x)/h}}}
Plug in our new values to the original equation and:
{{{h=d/((x/h)+((d-x)/h))}}}
Simplify, the x cancels and:
{{{h=d/(d/h)}}}
In order to go any further, we need to realize that {{{d/(d/h)}}} = {{{d*(d/h)^(-1)}}} and since {{{d}}} is really {{{d/1}}} we end up with:
{{{h=(d/1)*(d/h)^(-1)}}}
Negative exponents aren't as scary as they seem, we simply use the inverse, and get: {{{h=(d/1)*(h/d)}}}
Simplify and find that {{{d}}} cancels and our answer is: {{{h=h}}}
____________________________NEXT PART____________________________

(B) You did this in the last problem, #33 only used TAN.  Remember that COT is the inverse of TAN and to find COT on the calculator, just divide 1 by TAN.
But you are on the wrong side of the triangles!  Well, we know that a triangle totals 180 degrees and a right triangle uses a 90 degree; leaving us with two other angles to add up to 90 degrees and we have one angle for each triangle already!  What were they?
43.2 degrees and 51.4 degrees
Take one angle and subtract it from the remaining 90 degrees left over in our triangle, then repeat with the other:
cota={{{90-43.2=46.8}}} and cotb={{{90-51.4=38.6}}}
Now get out your calculators and start punching digits.
1/tan(46.8)~.94 and 1/tan(38.6)~1.25 (both to the nearest penny)
Back to our original problem, plug in the new numbers and we get:

{{{h=847/2.19=386}}}  The buildings are still about 386 feet apart.