Question

A taxi journey takes the passenger to a destination 8 km south and 3 kn west of its starting point. Find the distance and bearing of the destination from its starting point.

Using trigonometry.

Answer 1

Answer: We can use trigonometry to solve this problem.

First, let's draw a diagram to represent the situation:

|

|

| 8 km

|

|

--------X---------

| 3 km

|

|

|

|

The starting point is at the X, and the destination is 8 km south and 3 km west of the starting point.

To find the distance and bearing of the destination from the starting point, we can use the Pythagorean theorem and trigonometric functions.

The distance between the starting point and destination is the hypotenuse of a right triangle with legs of length 8 km (south) and 3 km (west). So we can use the Pythagorean theorem:

distance = √(8² + 3²) ≈ 8.6 km

To find the bearing (direction) of the destination from the starting point, we can use trigonometry. The bearing is the angle between the line connecting the starting point and destination and the line pointing due north.

We can use the tangent function to find this angle:

tan(θ) = opposite/adjacent = 3/8

θ = tan⁻¹(3/8) ≈ 20.56°

So the bearing of the destination from the starting point is approximately 20.56° west of due south.

Therefore, the distance of the destination from the starting point is approximately 8.6 km and the bearing of the destination from the starting point is approximately 20.56° west of due south.

Explanation: