Question

A life boat leaves a ship and floats 20 miles west and 9 miles north. If the ship's location represents the pole, what are the polar coordinates of the life boat?
A. (21.93, 65.77°)
B. (21.93, 114.23°)
C. (5.39, 65.77°)

Edit: This is high school mathematics; not sure why it says middle school.

Answer 1

Answer:

The polar coordinate of the boat is (21.93, 155.77°)

Step-by-step 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°)