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joe and dee are observing an island 5km apart.if joe looked north toward deeand turned...
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(Level 1) Associate Educator, Expert
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.
`(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)
Posted by mvcdc on May 13, 2013 at 5:54 PM (Answer #1)
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