Question

a car travels 250 km east, then turns 25° south of east and goes 115 km. what is the resultant distance traveled? ? km round to the nearest hundredth.

Explanation:

Step1: Split into x/y components

First leg (east): $x_1 = 250$ km, $y_1 = 0$ km
Second leg:
$x_2 = 115\cos(25^\circ) \approx 104.28$ km
$y_2 = 115\sin(25^\circ) \approx 48.67$ km

Step2: Sum components

Total $x = x_1 + x_2 = 250 + 104.28 = 354.28$ km
Total $y = y_1 + y_2 = 0 + 48.67 = 48.67$ km

Step3: Calculate resultant distance

$$ d = \sqrt{x^2 + y^2} = \sqrt{354.28^2 + 48.67^2} \approx 355.97 $$

Answer:

355.97 km