Question

A cell phone tower that is 150 ft tall sits on a mountain that

is 1200 ft above sea level. what is the angle of depression from
the top of the tower to a cell user 5 miles away and 400 ft above
sea level?

Answer 1

angle of elevation will be
`2.14^o.`

Explanation:

Given,

height of tower = 150 ft

height of tower = 1200 ft

So, total height of peak of tower = 1200 + 150

= 1350 ft

distance of user from cell tower = 5 miles

= 5 x 5280 feet

= 26,400 feet

Since the height of user from sea level = 400 ft

so, height of peak of tower with respect to user = 1350 - 400 ft

= 950 ft

If the angle of depression is assumed as
`\theta`, then we can write

`tan\theta\ =\ \frac{\textrm{height of peak of tower w.r.t user}}{\textrm{distance of user from tower}}`

`=>\ tan\theta\ =\ (950)/(26400)`

`=>\ tan\theta\ =\ 0.374`

`=>\ \theta\ =\ 2.14^o`

So, the angle of elevation will be
`2.14^o.`