A girl at a works 4 km South Ruby she then works 6 km West to c find the distance and bearing of c from a

Answer 1

To find the distance between points A and C, we can use the Pythagorean theorem as both the distance traveled south and west form a right triangle.

Given:
Distance traveled south (SA) = 4 km
Distance traveled west (AC) = 6 km

Using Pythagorean theorem:
AC^2 = SA^2 + AC^2
AC^2 = 4^2 + 6^2
AC^2 = 16 + 36
AC^2 = 52
AC = √52
AC ≈ 7.21 km

Now, to find the bearing of point C from A, we need to find the angle θ formed from the direction north (up) to the line segment AC.

θ = arctan(4/6)
θ ≈ arctan(0.667)
θ ≈ 33.69 degrees

Therefore, the distance between points A and C is approximately 7.21 km and the bearing of point C from A is approximately 33.69 degrees.