I am having trouble solving this word problem:
A cellular tower that is $150\text{ ft}$ is placed on top of a mountain that is $1200\text{ ft}$ above sea level. What is the angle of depression from the top of the tower to a cell phone user who is $5$ horizontal miles away and $400$ feet above sea level?
Here is my attempt:
opposite side = $5$ miles = $26400\text{ ft}$
adjacent side = $950\text{ ft}$
so $$\tan(?) = \frac{26400\text{ ft}} { 950\text{ ft}},$$ and $\arctan$ should give us the angle.
$$\arctan\frac{26400\text{ ft}}{950\text{ ft}} = 87.94^\circ.$$ This angle is the one with mountain and a slope to the head of the user. Thus an angle of depression as it is an angle formed between the horizontal line and that slope which is equal to $90^\circ-87.94^\circ = 2.06^\circ$.
What am I doing wrong?
Here is a sketch of the problem I made, did I interpret it wrong?