Please help me with this math prob, it involves cosine and sine rule in a triangle?

Question

A rally car dives at 140 km/h for 45 mins on a bearing of 032 degrees and then 180 km/h for 40 mins on a bearing 317 degrees. FInd the distance and bearing of the car from its starting point.

Please give me a step by step answer please thank you

Answer 1

Look at these problems as two seperate parts. I hope you learnt how to add vectors also.

For the first part determine how long he traveled.

140km/60min * 45min = 105km

Find the horizontal and vertical components of this vector.

Horizontal x = 105 * cos 32 = 89 km
Vertical y = 105 * sin 32 = 55.6 km

Do the same for the other.
For this one you have an angle of -43 or 317
Since this is in the fourth quadrant the x is positive and y is negative.

Find out how far he traveled
180km/60min * 40min = 120km

Horizontal component x = 120 * cos -43 = 87.8
Vertical component y = 120 * sin -43 = -81.8

To find his destination just add the two vectors

xfinal = 89 + 87.8
yfinal = 55.6 + (- 81.8)

To find the distance his end point is use the pythagorean theorem.x^2 + y^2 = d^2