# calculus

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A lifeguard was staring at a ship in the distance, and watched the smokestack as the ship went out to sea. The lifeguard's eye level is 4 meters above sea level. If the height of the smoke stack above water is 30 meters and the radius of earth is about 6400km, how far off from the shore would the ship be when the lifeguard who loose sight of it.

how should I start this?

• calculus -

I visualize a circle with radius 6400 and the ship at a point P.
let the eyes of the lifeguard be Q.
then Q is 6400.004 km from the centre of our earth circle.
let PQ = x
x^2 + 6400^2 = 6400.004^2

I got x = appr. 7.155 km

• calculus -

the answer is suppose to be 2675.3
..

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