don and dee are 5km apart and observing an island.If dee looked north toward don and turned 22.3degrees east,she would see the island.If don looked south toward dee and turned 49.5degrees east he...

don and dee are 5km apart and observing an island.If dee looked north toward don and turned 22.3degrees east,she would see the island.If don looked south toward dee and turned 49.5degrees east he would see the island.How far is dee from the island and how far is don from island?

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See attached diagram for pictorial depcition of the problem.

In order to find `d_1` and `d_2` we will use the sine law which states that:

`a/sinA=b/sinB=c/sinC`

Where the angle (A,B,C) is the one opposite the side (a,b,c).

First we must solve for the angle that is opposite the side whose length we know:

I = 180-22.3-49.5 = 88.2 deg

Now we can solve for `d_1` and `d_2` :

`d_1/sin49.5=5/sin88.2` 

`d_1=5sin49.5/sin88.2=3.8`

and:

`d_2/sin22.3=5/sin88.2` 

`d_2=5sin22.3/sin88.2=1.9`

Therefore, Dee is 3.8 km from the island and Don is 1.9 km from the island.

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