Question

A fire truck is en route to an address that is six blocks east and five blocks north of the fire station. Using the fire station as the pole and the east direction as the polar axis, express the fire truck's destination in polar coordinates. Round the coordinates to the nearest hundredth. Express θ in degrees.

Answer 1

(We have to assume the blocks are square.) The Pythagorean theorem gives the radial distance (d).
d = √(6² + 5²) = √61 ≈ 7.81 . . . blocks

The tangent of the angle (θ) is the ratio of northerly distance to easterly distance.
tan(θ) = 5/6
θ = arctan(5/6) ≈ 39.81°

The polar coordinates of the address are 7.81∠39.81°.