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.

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°)

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3