A train travels 96km on a bearing of 45°. It turns south bound . How far east has it gone?

Femcy991

3 years ago

To find how far east the train has gone, we need to determine the horizontal component of its displacement after it turns south.

Given that the train travels 96 km on a bearing of 45°, we can use trigonometry to find the eastward and northward components of its displacement.

The eastward component can be calculated using the cosine function, while the northward component can be determined using the sine function.

Let's calculate the eastward component:

Eastward component = Displacement × cos(Bearing)
Eastward component = 96 km × cos(45°)

Eastward component ≈ 96 km × 0.7071

Eastward component ≈ 67.97 km (rounded to two decimal places)

Therefore, the train has gone approximately 67.97 km east.