Question

a car drives 250 km east, then turns 25° south of east and drives 115 km. how far is the car from its start?
250 km
25°
115 km
? km
round to the nearest hundredth.

Explanation:

Step1: Calculate total eastward distance

$d_x = 250 + 115\times\cos(25^\circ) \approx 250 + 115\times0.9063 = 250 + 104.2245 = 354.2245$ km

Step2: Calculate total southward distance

$d_y = 115\times\sin(25^\circ) \approx 115\times0.4226 = 48.599$ km

Step3: Compute straight-line distance

$$d = \sqrt{d_x^2 + d_y^2} \approx \sqrt{(354.2245)^2 + (48.599)^2} \approx \sqrt{125475.0 + 2361.86} \approx \sqrt{127836.86} \approx 357.54$$

Answer:

$\boldsymbol{357.54}$ km