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Answer:
Commutative
Step-by-step explanation:
There are four basic property of operations to solve an algebraic expressions. They are associative, commutative, distributive and identity.
The expression given is :
So the given algebraic expression is a commutative property of operations. The commutative property states that when any two numbers are added in an expression the sum of the numbers are the same regardless of the order of the numbers that are added.
Thus the sum of the above expression will be same in which ever order the numbers are added.
By using the given distances and directions, we have;
Part A: 1083.5 feet
Part B: 1921.37 feet
Part C: 58.05°
<h3>How can the distances and directions be calculated?</h3>The distance between David and Lacey = 2000 feet
David's angle to the boat = 70°
Lacey's angle to the boat = 32°
Part A
The distance of the boat from David is found as follows;
Imaginary lines drawn from the boat to David and then to Lacey form a triangle.
In the triangle, let <em>A</em><em> </em>= 70°
B = 32°
Therefore by the sum of angles in a triangle, we have;
C = 180° - (70° + 32°) = 78°
By using sine rule we have;
David's distance from the boat, <em>b</em>, is therefore;
The angle subtended by the coastline, <em>C</em>, is therefore;
- David's distance from the boat is 1083.5 feet
Part B
The distance between the boat and Lacey is found as follows;
- Lacey's distance from the boat is 1921.37 feet
Part C
When <em>b </em>= 1200 feet, we have;
Finding the vertical distance of the boat from the coastline, we have;
1083.5 × sin(70) = 1018.17
We have;
The angle between the coastline and his view to the boat, <em>B'</em>, is therefore;
- B' = arcsine (1018.17÷1200) = 58.05°
Learn more about sine rule here:
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