First, let's calculate the distance traveled.
52 x 5 = 260 miles
Assuming that the car begins at the origin (0,0), travelling 33˚ south of west means it travels in the direction of Quadrant 3, and the angle closest to the origin is 33˚.
If we allow a line to be drawn down from the X-axis to the ending point, we form a right triangle with hypotenuse of length 260. Since we know one angle to be 33˚ and another to be 90˚, the last interior angle must be 57˚. Now we need to find the side lengths of the triangle, these side lengths, will be the coordinates of the destination of the car. To do this, we can create an equation with one unknown using the sin or cos functions.
Let's label the sides of the triangle X and Y.
sin(θ) = opposite / hypotenuse
sin(33˚) = Y / 260
141.6 ≈ Y
cos(θ) = adjacent / hypotenuse
cos(33˚) = X / 260
218.1 ≈ X
So the coordinates of the car's destination are approximately (-218.1,-141.6)
[The coordinates are negative because the car is in Quadrant 3]
