Trig Application / Modulus Q's Help!

[luken93]

I can't remember the question exactly, but I think this is how it goes:
A man was standing at sea level, and looked up to the tip of a mountain at an angle of 30 degrees of elevation (blue angle)
He then walked 500m towards the mountain, and was now standing at 50m above sea level, and the tip of the mountain was now at 40 degress of elevation (red angle)

It looked something like this:
[IMG]http://img121.imageshack.us/img121/3049/39306926.jpg[/img]

Then the questions were:
a) Find the value of x
b) Find the value of d in terms of h
c) Find y in terms of h
d) Hence, find the value of h

Thanks

[luken93]

I have another question, can someone please show the steps to transform:
reflected on the line
The examples in the book with the dont really make sense, and does the apostrophe stand for image?

Also, Are there rules to show transformations of any kind when doing these sort of questions (ie. reflections, dilations, vector movement)

PS If anyone can answer the first question I posted that'd be great also!

Thanks

[TrueTears]

I have another question, can someone please show the steps to transform:
reflected on the line
Thanks

(x,y) -> (-y,-x)

x' = -y and y' = -x

-x' = y and -y' = x

=> y=|x| -> -x' = |-y'| -> -x'=|y'|

therefore the transformed graph is -x=|y| this is in implicit form, theres no real need to change it into explicit form.

[luken93]

(x,y) -> (-y,-x)

ok thanks for that, i understand how you did the rest of it, but why do you swap the x and y around in the brackets?
is it just because for the line y = -x, so you just rearrange to match each one (y=-x) and (x=-y)?

Also, the answers to the first q are:
a)
b)
c)
d) ? (I couldn't get this one for some reason, kept getting a negative answer?

[TrueTears]

yeah you can prove it geometrically or derive it from a previous known result eg, reflecting in line y=x interchanges x and y, so reflecting in y = -x interchanges x and y again but both are negated.

[luken93]

yeah you can prove it geometrically or derive it from a previous known result eg, reflecting in line y=x interchanges x and y, so reflecting in y = -x interchanges x and y again but both are negated.

yep thought so, just wanted to check!