How far did the rocket rise during those four seconds?

A rocket shoots straight up from the launchpad. Five seconds after liftoff, an observer two miles away notes that the rocket's angle of elevation is 3.5 degrees. Four seconds later, the angle of elevation is 41 degrees.

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The rockets takes off vertically upwards from the launchpad. An observer 2 miles away measures the angle of elevation of the rocket as 3.5 degrees after 5 seconds as 3.5 degrees. After 9 seconds it is 41 degrees.

The rocket, launchpad and the observer form a right angled triangle. If the height of the rocket is h1 after 5 seconds and h2 after 9 seconds:

`tan 4.5 = (h1)/2` and `tan 41 = (h2)/2`

=> `h1 = 2*tan 4.5` and `h2 = 2*tan 41`

`h2 - h1 = 2*(tan 41 - tan 4.5) = 1.581`

The rocket rises by 1.581 miles during the 4 seconds.

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