Answer:
Approximately 1,320 feet.
Step-by-step explanation:
Let one person be x miles from the skycraper, then the other one will be 5 - x miles away from it.
So we have the 2 equations:
tan 4 = h/x
tan 10 = h/(5 - x) where h is the height of the skyscraper
From the first equation:
h = x tan 4
Substituting in the second equation:
tan 10 = x tan 4 / (5 - x)
5 tan 10 - x tan 10 = x tan 4
x tan 10 + x tan 4 = 5 tan 10
x = 5 tan 10 / ( tan 10 + tan 4)
= 3.58 miles
h = 3.58 * tan 4
= 0.25 miles
= 1320 feet approx.
