A surveyor needs to determine the distance across the pond as shown in the diagram. He determines that the distance from his pos
ition to point y on the south shore of the pond is 200 meters and the angle from his position to point x on the north shore is 32°. What is the distance, to the nearest meter, across the pond?
After Reading the question we can draw the figure which is triangle XPS
given below.
The point S denotes the Surveyor who is at distance 200 from the south shore(P) and this point P is at y distance from North shore (X) and also the angle given is 32 degree.
1 step:, , then . 2 step:, then and will have form . 3 step: Solve this system and dividing first equation on second we obtain . So, and , - the common ratio. 4 step: Insert into equation and obtain , from where .
, 
, then
.
, then 
will have form 
.
and dividing first equation on second we obtain 
. So, 
and 
, 
- the common ratio.
and obtain 
, from where 
.