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. How far did the rocket rise during those four seconds?
Solution
Draw a right triangle where the base edge is length 2. The base angle will be 3.5 degrees, and so we can use Tan(3.5) = x/2 . After plugging this into your calculator, you should find that x = .122. This means the rocket has traveled .122 miles into the air. Now draw another triangle that looks exactly the same as the first triangle, except this one will have a base angle of 41 degrees. We can set up the same formula where Tan(41) = x/2. Solving this equation for x, we find that x = 1.739. To find out how much the rocket traveled in 5 seconds, take the second value for x, 1.739, and the first value for x , .122, and subtract. You should find that the rocket traveled 1.616 miles.
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A rocket shoots straight up from the launchpad- Five seconds after lif.docx
1. 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. How far did the rocket rise during those four seconds?
Solution
Draw a right triangle where the base edge is length 2. The base angle will be 3.5 degrees, and so
we can use Tan(3.5) = x/2 . After plugging this into your calculator, you should find that x =
.122. This means the rocket has traveled .122 miles into the air. Now draw another triangle that
looks exactly the same as the first triangle, except this one will have a base angle of 41 degrees.
We can set up the same formula where Tan(41) = x/2. Solving this equation for x, we find that x
= 1.739. To find out how much the rocket traveled in 5 seconds, take the second value for x,
1.739, and the first value for x , .122, and subtract. You should find that the rocket traveled 1.616
miles.
