We appreciate your visit to Apex is 7 miles south of Mooresville Shotwell is due east of Apex and is located south 75 east from Mooresville A How far is. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The distance between Apex and Shotwell can be found using the law of cosines. The bearing from Mooresville to Shotwell is [tex]105°[/tex]. The bearing from Shotwell to Morrisville is [tex]285°[/tex].
A) To find the distance between Apex and Shotwell, we can use the law of cosines.
Let's call the distance between Apex and Shotwell x.
Since Apex is 7 miles south of Mooresville, the distance between Mooresville and Shotwell is x + 7.
From the given information, we know that the angle between Apex and Mooresville is 75.
[tex]x^2 = (x + 7)^2 + 7^2 - 2(x + 7)(7)√3/2 cos(75°)[/tex]
Simplifying the equation and solving for x will give us the distance between Apex and Shotwell.
B) The bearing from Mooresville to Shotwell can be found by subtracting the given angle of [tex]75°[/tex]from [tex]180°[/tex] (since [tex]180°[/tex] represents due south). The bearing will be[tex]180° - 75° = 105°[/tex].
C) The bearing from Shotwell to Mooresville will be the opposite direction of the bearing from Mooresville to Shotwell, which is [tex]285°[/tex].
D) Similar to B), the bearing from Mooresville to Apex will be [tex]180° - 75° = 105°[/tex].
E) The bearing from Apex to Mooresville will be the opposite direction of the bearing from Mooresville to Apex, which is [tex]285°[/tex].
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