Answer:
The polar coordinate of the boat is (21.93, 155.77°)
Explanation:
If a A life boat leaves a ship and floats 20 miles west and 9 miles north, the boat must have move 20miles in the x direction and 9miles in the x direction.
In order to get the polar coordinate of the life boat, we need to find the resultant and the direction the coast is moving.
Using the formula to find the resultant
R = √x²+y²
R = √(-20)²+9²
R = √400+81
R = √481
R = 21.93miles
The direction is gotten using the formula;
Theta = arctan y/x
theta = arctan (9/-20)
theta = arctan -0.45
theta = -24.23°
Note that the x is negative because the boat moves towards the west (negative x direction)
Note that tan is negative in the second quadrant. In the second quadrant, the angle will become 180-24.23 = 155.77°
The polar coordinate of the boat is (21.93, 155.77°)