The distance d in miles that can be seen on the surface of the ocean is given by d = 1.6 h, where h
is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to
see a distance of 19.5 miles?
Your formula is wrong. See
http://en.wikipedia.org/wiki/Horizon
There should be a square root sign for the h, or possibly for the 1.6 h.
That source says:
d = 1.323 sqrt(h)
when h is in feet and d is in miles.
Recheck your problem statement.
Once you, "plug in" d = 19.5 miles and calculate h.
I think you meant √(1.6h).
So you have
√(1.6h) = 19.5
square both sides
1.6h = 19.5^2=380.25
h=237.6'
or 238' to the nearest foot.
To find the height, h, in feet, we can rearrange the equation:
d = 1.6h
Given that the distance, d, is 19.5 miles, we can substitute this value into the equation:
19.5 = 1.6h
To solve for h, we divide both sides of the equation by 1.6:
h = 19.5 / 1.6
Using a calculator, we find:
h ≈ 12.19 feet
Therefore, a platform would have to be approximately 12 feet high to see a distance of 19.5 miles on the surface of the ocean.
To find the height of the platform, we can plug in the given values into the equation d = 1.6h. In this case, we want to find the height (h) when the distance (d) is 19.5 miles.
Substituting the values into the equation:
19.5 = 1.6h
To solve for h, we need to isolate the variable h.
Divide both sides of the equation by 1.6:
19.5 / 1.6 = h
Calculating the division:
h ≈ 12.19 feet
Therefore, to the nearest foot, the platform would have to be approximately 12 feet high to see a distance of 19.5 miles on the surface of the ocean.