a car drives 30km on a course 215degree T. how far west is it of its starting point?

Question

the course is 215 degree and T is listed next to it. I don't know what this means and I hope someone can help me with this. the 215 degree T has to deal with True bearings. pls do let me know your answer.

Answer 1

bearing is always the angle away from north

draw a coordinate axes

from the upper part of the y-axis, draw an arc of 215º

this brings you 35º into the third quadrant (215-180=35)

draw a diagonal line (35º into the third quadrant), southwest and label it 35 km

from the endpoint of this segment draw a vertical line upwards perpendicular to the x-axis

you now have a right triangle with the 35 km segment as the hypotenuse, the vertical line as one leg, and the distance from the origin to the point where the vertical line meets the x-axis as the other leg

the x-axis distance is the distance you want, the distance how far west from the starting point the car is

the acute angle at the top right of the triangle near the origin is the angle to use along with the cosine function

what is the degree measure of this angle ?

you went 35º into the third quadrant when you made the 215º arc

that leaves 90-35=55º for the acute angle

cos=adjacent/hypotenuse

call the x-axis distance "x"

cos55º=x/30

cos55º*30=x

0.573576*30=x

17.20728 km=x

the car is 17.20728 km west of its starting point (round to whatever place you need)