# joe and dee are observing an island 5km apart.if joe looked north toward deeand turned 22.3degrees to the east she would see the island .if dee looked south toward joe and turned 49.5deg east she...

joe and dee are observing an island 5km apart.if joe looked north toward deeand turned 22.3degrees to the east she would see the island .if dee looked south toward joe and turned 49.5deg east she saw island how far is dee and how far is joe from island

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Let us say that Dee is at point D and Joe at point J, while the island is at point I. These there points create a triangle, DJI. The length of segment DJ = 5.

Angle J = 22.3 degrees (since Joe looks at Dee and turns this angle to see the island)

Angle D = 49.5 degrees.

The third angle, Angle I, can easily be calculated: 180 - 49.5 - 22.3 = 102.8 degrees (sum of angles in a triangle is 180).

Now, we want to solve for distance DI and JI. This is an application of the Laws of Sine:

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

Or basically that the ratio of the angle measures to the opposite side in a triangle is constant.

In this case:

Angle I is opposite JD

Angle J is poosite DI

Angle D is opposite JI.

Hence,

`(sin(22.3))/(DI) = (sin(49.5))/(JI) = (sin(102.8))/5 = 0.195`

Using these relationships, we see that:

DI = 0.195/sin(22.3) = 2.04 (Dee from Island)

JI = 0.195/sin(49.5) = 3.90 (Joe from Island)