# Two cabins in a valley are viewed from the top of a cliff. Assume that the cabins and the base of the cliff are on a line and the observer is 2000ft above the valley floor. The angles of depression to the cabins are 31 degrees and 48 degrees respectively. How far are the cabins from each other?

1
by samfunte

2015-02-14T21:39:43+08:00
i hope the cabins is align from the y axis because if the cabins is align in x axis this is a difficult problem so we solve this and assume that the cabins is align in y axis

let x the distance from the base to the first cabin
y is the distance from the base to the second cabin
and  d is the distance from the observer to the cabin and it the same from the two cabins because the observer do not move.
d = 2000ft
use tangent to solve this problem

so for the first cabin let use 48 angle
tan 48 = x /2000
then
x = 2221.23

for second cabin
tan 31 = y/ 2000
then
y =1201. 72

so the distance between the cabins is
2221.23 - 1201.72 = 1019. 51 ft

I hope this is correct!