We will solve this problem by applying basic trigonometry and vector calculations. Here's the breakdown:

Part 1: Distance from the starting point

The car follows two movements:

1. First leg: 25 miles at a bearing of 35°.
2. Second leg: Turns 90° to the right and travels 35 miles.

We will treat this as a triangle and use the law of cosines to find the final distance from the starting point.

Step 1: Resolve the first leg into components

We can break the first leg into two components (north-south and east-west):

• North-South: $25 \times \cos(35^\circ)$
• East-West: $25 \times \sin(35^\circ)$

Step 2: Second leg

Since the car turns 90° to the right, the second leg is perpendicular to the first. This creates a right angle at the turn. The second leg is entirely horizontal (east-west), adding to the east-west displacement:

• North-South displacement: $25 \times \cos(35^\circ)$ (unchanged)
• East-West displacement: $25 \times \sin(35^\circ) + 35$

Step 3: Final distance using the Pythagorean theorem

We now calculate the total displacement using the Pythagorean theorem: $\text{Total distance} = \sqrt{ \left( 25 \times \cos(35^\circ) \right)^2 + \left( 25 \times \sin(35^\circ) + 35 \right)^2 }$

Let's calculate that.The total distance of the car from its starting point is approximately 53.42 miles.

Part 2: Bearing from the start point to the end point

To calculate the bearing from the starting point to the end point, we use the formula for the bearing angle: $\text{Bearing} = \arctan\left(\frac{\text{East-West displacement}}{\text{North-South displacement}}\right)$ This will give us the angle relative to the north-south line, which we will adjust based on the quadrant.

Let's calculate the bearing now.The bearing from the starting point to the end point is approximately 67°.

Summary:

• The distance of the car from the starting point is 53.42 miles.
• The bearing from the starting point to the end point is 67° (to the nearest degree).

Do you need further details or clarifications on the process?

Here are 5 related questions you might find helpful:

1. How would the result change if the second leg was longer or shorter?
2. How does the law of cosines apply when solving non-right triangles in general?
3. What if the bearing turned 45° instead of 90°? How would the calculation change?
4. Could this problem be solved graphically using a coordinate system?
5. How does the sine rule help in solving similar navigation problems?

Tip: Always double-check the units of your angles when switching between degrees and radians in trigonometry calculations.