SOLUTION: The higher a lookout tower is built, the farther an observer can see. That distance d (called the horizon distance, measured in miles) is related to the height h of the observer (m

Algebra ->  Radicals -> SOLUTION: The higher a lookout tower is built, the farther an observer can see. That distance d (called the horizon distance, measured in miles) is related to the height h of the observer (m      Log On


   

Question 1168410: The higher a lookout tower is built, the farther an observer can see. That distance d (called the horizon distance, measured in miles) is related to the height h of the observer (measured in feet) by the formula
d = 1.4 radical symbol with h under it



How tall (in ft) must a lookout tower be to see the edge of the forest, 23 miles away? (Round your answer to the nearest foot.)
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
d=1.4 sqrt(h)=23
sqrt(h)=23/1.4=16.43
h=269.90 or 270 feet
(I generally use 1.1 sqrt(h)

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

For the Earth conditions,  the correct formula is

        d = 1.22459%2Asqrt%28h%29   miles,   with  h  in feet.


See,  for example,  this source

https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf

https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf