Question 1173735
Let's break down this problem step-by-step.

**1. Visualize the Problem**

* **A to B:** 320 miles, bearing S40°E
* **A to C:** Due East, 210 mph for 1 hour
* **C to B:** We need to find the distance and bearing.

**2. Calculate the Distance from A to C**

* Distance = Speed * Time
* Distance AC = 210 mph * 1 hour = 210 miles

**3. Set Up a Coordinate System**

* Let A be the origin (0, 0).
* Since AC is due East, point C is (210, 0).
* To find the coordinates of B, we need to use the distance and bearing from A to B.

**4. Find the Coordinates of B**

* Bearing S40°E means 40 degrees east of south.
* We can use trigonometry to find the coordinates:
    * x-coordinate (Eastward): 320 * sin(40°)
    * y-coordinate (Southward): 320 * cos(40°)
* Calculate:
    * x = 320 * sin(40°) ≈ 205.67 miles
    * y = 320 * cos(40°) ≈ 245.13 miles
* Since it's S40°E, the coordinates of B are (205.67, -245.13).

**5. Find the Distance from C to B**

* Use the distance formula:
    * CB = √[(x2 - x1)² + (y2 - y1)²]
    * CB = √[(205.67 - 210)² + (-245.13 - 0)²]
    * CB = √[(-4.33)² + (-245.13)²]
    * CB = √[18.75 + 60088.66]
    * CB = √60107.41
    * CB ≈ 245.17 miles

* Rounded to the nearest mile, CB ≈ 245 miles.

**6. Find the Bearing from C to B**

* We need to find the angle between the East direction from C and the line CB.
* Use the tangent function:
    * tan(θ) = |y-coordinate| / |x-coordinate|
    * tan(θ) = 245.13 / 4.33
    * tan(θ) ≈ 56.61
    * θ = arctan(56.61) ≈ 88.99 degrees
* Since B is south and slightly west of C, the bearing is approximately S89°W.

**Final Answers**

* **Distance (CB):** Approximately 245 miles
* **Bearing (C to B):** Approximately S89°W