how can i solve this?

Question

4. A rescue helicopter was sent to retrieve passengers off a ship. When the helicopter, which is 0.5 miles above the water, passes over a buoy that is 1.1 miles from the shore, the angle formed by the shore, the helicopter and the ship is 90. Answer the following and show all work. (Section 7.3)

A. How far is the ship from the buoy? Round your answer to the nearest tenth of a mile.

B. How far is the ship to the shore line?

 

 

Answer 1

Hello!

 

Let's think about this problem a bit.

 

First, we see that this problem asks us about distances between various objects.  This tells us that a good first step would be to draw a picture.  So, go ahead and make a sketch of the problem.  Your sketch should include all relevant objects (the helicopter, the buoy, the ship, and the shore).  It should also be consistent with the problem statement.  For example, the helicopter passes over the buoy on its way to the ship, so the ship should be farther from the shore than the buoy.

 

Now that we can picture what's going on, let's add some extra information to the sketch.

• The buoy should be level with the water, so the helicopter must be 0.5 miles above the buoy.
• We know the buoy is 1.1 miles from the shore.
• We know the angle formed by the shore, the helicopter, and the ship.

 

We should also ask ourselves if there's any information we know that wasn't given explicitly.  For example, what is the angle formed by the shore, the buoy, and the helicopter?

 

Finally, we should notice that there are some triangles waiting to be drawn: we should connect each of the four objects in our sketch to the other three using straight lines (the ship, buoy, and shore will all be on the same line).  Any triangle sides of unknown length should now be labeled with a variable.

 

Now that we have a complete sketch, we're ready to solve the problem.

 

First, the helicopter-buoy-shore triangle has just one missing side length.  You should be able to calculate it.  (Hint: what kind of triangle is this?)

 

Now, the lengths we don't know correspond to the distance between the helicopter and the ship, and the distance between the ship and the buoy.  Based on your sketch, write two equations involving these unknown distances.  (Hint: each unknown appears as part of a squared quantity in each equation.)

 

We now have a system of nonlinear equations to solve.  Your textbook should have a number of examples to help you from here, but feel free to post again with your progress if you get stuck!