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...

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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.**