The tourist is at the top of a mountain which we shall call point T, and he looks down at a deer which is 150 feet away from the bottom of the mountain. The deer is at point D while the bottom of the mountain is point B. The tourist nneds to look down in order to take a photograph of the deer an to do this, he needs to look downwards at an angle labelled as angle x.
The diagram formed by all three points TBD is a right angled triangleand we shall apply the trigonometric ratios to this.
The reference angle shall be taken as angle x, and that makes the line BD (150 ft) to be the opposite side while line TB (60 ft) is the adjacent side. Note that the opposite side is the side facing the reference angle (angle x in this case) and the adjacent side is the line that lies between the reference angle and the 90 degree angle.
Having identified the opposite and adjacent sides the ratio to be applied shall be;
Tan x = opposite/adjacent
Tan x = 150/60
Tan x = 2.5000
Checking the table of values or by using a calculator, (check under 2nd Function of Tan), your x becomes
x = 68.1985...
x is approximately 68.2 degrees (rounded to the nearest degree)