Illustrate and solve. A monument near a dock is 12 miles east of a ship. After the ship has sailed 7 miles, the monument bears N62degreesE. In what direction is the ship sailing?
I have helped you with 3 out of your 4 questions, they are all similar to each other.
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the triangle show with sides 12 and 7 and co-contained angle of 62 degrees adjascent to 12 sides by sin law: sin@/12=sin62/7 is this correct
I assume that the bearing is from the position of the ship. Then the angle opposite the 7 side is 18 degrees.
Sin@/12 = sin18/7
Gives you the bottom angle
To solve this problem, we need to use the concepts of trigonometry and vectors.
Let's visualize the situation. Imagine a coordinate system with the dock located at the origin (0, 0). The ship starts at (0, 0) and sails 7 miles in an unknown direction, while the monument is 12 miles away from the ship and bears N62°E from its position.
First, let's determine the position of the monument relative to the dock. Since the monument is 12 miles east of the ship, its coordinates would be (12, 0).
Next, let's consider the bearing of the monument from the ship. The bearing N62°E means that the angle formed between the direction of the monument and the north direction is 62°, measured clockwise.
To find the direction of the ship's sailing, we can calculate the bearing of the monument from the ship's position before it moves.
Using the concept of vector addition, we can find the position of the ship after sailing 7 miles:
Ship's position after sailing = (0, 0) + (7, 0) = (7, 0)
Now, we need to find the bearing of the monument (located at (12, 0)) from the ship's new position.
To do this, we can determine the angle formed between the direction of the monument and the line connecting the ship's new position and the monument.
Using trigonometry, we can calculate the angle:
Tan(angle) = (Y_distance / X_distance)
Substituting the values:
Tan(angle) = (0 - 0) / (12 - 7) = 0 / 5 = 0
Since the tangent of the angle is zero, the angle itself is also zero.
Therefore, the direction in which the ship is sailing is N0°E (straight north).
So, the ship is sailing in the north direction.