I cannot fit the whole question in this box.

Question

The approximate distance (in meters) to the horizon is 3600 times the square root of your height (in meters) above the surface of the Earth. If you stand in the rigging of a tall sailboat 36m above the water, how far away is the horizon?

Answer 1

Sounds like similar triangles to me:

h/(3600√h) = (36 + h)/x

Cross multiplying gives:

3600√h(h + 36) = hx

x = 3600√h(h + 36)/h

Answer 2

Hi Lottie!

For this problem its helpful to try to convert the written descriptions into a formula. This can be easier said than done of course. What we know is that the distance to the horizon, lets call this "d", is 3600 times the square root of your height, which let's call "h". This means that:

d is 3600 times square-root(h)

or

d = 3600 * sqrt(h)

If your problem has the height of the person, p, in the scenario then the total height, h, would be 36 + p. If you plug this into the formula you get

d = 3600 * sqrt(36 + p)

If the problem doesn't give you the persons height I'd assume that they just want you to solve it for p=0 (h=36). With this equation you should be able to plug the correct values in and get your distance. Hope this helps!

-Nathan