a car travels due south for 3km the due east for 8km. What is the true bearing of the car from the starting point?
111 degrees true
what is arctan(8/3) E of S?
46
To find the true bearing of the car from the starting point, you need to use the concept of trigonometry and the tangent function.
First, visualize the situation. The car travels 3 km due south, so it moves downward 3 km on a grid. Then, it travels 8 km due east, moving to the right 8 km on the same grid.
Next, draw a right triangle based on the movement of the car:
- One side of the triangle represents the 3 km movement south.
- Another side represents the 8 km movement east.
- The hypotenuse of the triangle represents the straight-line distance between the car and the starting point.
Once the triangle is drawn, you can calculate the true bearing of the car using the tangent function. Here are the steps:
1. Identify the triangle angles:
- The angle between the south direction and the hypotenuse is the desired bearing.
- The angle between the south direction and the adjacent side is 90 degrees (because south is perpendicular to east).
2. Use the tangent function:
- The tangent of the desired bearing (B) is equal to the opposite side (south movement) divided by the adjacent side (east movement).
- In this case, tan(B) = 3/8.
3. Solve for B:
- Take the inverse tangent (arctan) of both sides to find the angle B.
- B = arctan(3/8) ≈ 20.56 degrees.
4. Determine the true bearing:
- The true bearing of the car from the starting point is 180 degrees (south) + 20.56 degrees (angle B) = 200.56 degrees.
Therefore, the true bearing of the car from the starting point is approximately 200.56 degrees.