A ship is first seen on a radar screen to be 9 km east of the radar site. Some time later, the ship is 18 km northwest. What is the displacement of the ship from the first location it is seen at?
http://www.jiskha.com/display.cgi?id=1478363831
sideA=18
sideB=9
AngleC=135 degrees
c^2=a^2+b^2-2abcosC
solve for c.
How did you determine the angle?
To find the displacement of the ship from the first location it is seen at, we can use the Pythagorean theorem.
Step 1: Draw a diagram to visualize the problem. Let's assume the radar site is at point A and the first location where the ship is seen is point B.
B (9 km east)
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A
Step 2: Determine the distance the ship has moved in the east direction. From the information given, we know that the ship is first seen 9 km east of the radar site. Therefore, the ship has moved 9 km in the east direction.
Step 3: Determine the distance the ship has moved in the northwest direction. From the information given, we know that the ship is later seen 18 km northwest of the radar site. To find the distance moved in the northwest direction, we need to split the displacement into horizontal and vertical components.
B (9 km east)
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A
Let's define the horizontal component as x and the vertical component as y. Then, using basic trigonometry, we can determine the values of x and y.
x = 18 km * cos(45°)
y = 18 km * sin(45°)
Using these formulas, we find:
x ≈ 12.73 km
y ≈ 12.73 km
So, the ship has moved approximately 12.73 km horizontally (in the east direction) and 12.73 km vertically (in the northwest direction).
Step 4: Use the Pythagorean theorem to find the displacement.
The displacement of the ship can be found by calculating the hypotenuse of the right-angled triangle formed by the horizontal and vertical components of the displacement.
Applying the Pythagorean theorem:
Displacement = √(9 km)^2 + (12.73 km)^2
Simplifying the equation:
Displacement = √(81 km^2 + 161.97 km^2)
Displacement = √(242.97 km^2)
Displacement ≈ 15.59 km
Therefore, the displacement of the ship from the first location it is seen at is approximately 15.59 km.