Hello, Adam!
It would help if your punctuation grammar were better . . .
From a given position an observer notes that the angle of elevation of a rock is 47°.
After walking 1000 ft towards the rock up a slope of 32°,
he finds the angle of elevation to be 75°.
Find the vertical distance of the rock above each point of observation. Code:
* R
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 47° 
**
A B
The observer is at $\displaystyle A$.
. . The rock is at $\displaystyle R$.
. . $\displaystyle \angle RAB = 47^o$
We are asked to find $\displaystyle RB$.
Code:
* R

o

o 

o 
75°
o* C
1000 * P 
* 
* 32° 
**
A B
The observer walk 1000 ft up the 32°slope to point $\displaystyle P$.
From there, the angle of elevation to $\displaystyle R$ is: $\displaystyle \angle RPC = 75^o$.
We are asked to find $\displaystyle RC$.