1. ## Technical trig question......

Hi,
I have a trig question here which someone has tried to explain to me but I just cant follow what's going on with it. Can someone please attempt this and explain it in simple terms what each step is leading to. I've attached an image to make sure the question is understood correctly.

Thanks
David

2. Hi Splint

Maybe you can write the explanation you got and state the part that you don't understand

3. OK, this was the reply:

................................................… |D
................................................… | h
................................................… |
A ------- d ------- B ------ x ------ C

let angle DAC =p and angle DBC = q
take BC = x

tan p = h/(x+b)
x + b = h cot p ----------------- (1) (that's a typo, should be x+d)

tan q = h/x
x = h cot q ------------------ (2)
subtract > (1) - (2) to get rid of x
b = h[cot p - cot q] (that's another typo, should be d=)
b = h[tab q - tan p]/tan p tan q (that's another typo, should be d=)
h = b tan p tan q/[tan q - tan p] (that's another typo, should be =d)

I've identified the typos myself but appart from that it is how the answer was written. It's the last two lines which I cant follow.

4. Hi Splint

$\cot p - \cot q$

$=\frac{1}{\tan p}-\frac{1}{\tan q}$

$=\frac{\tan q-\tan p}{\tan p~\tan q}$