# A car is driven 200 km west and then 80 km southwest. What is the displacement of the car from the point of o

I don't know how to do this . . . there are no given angles that I can plug into some equation, how do I solve this?

Update:

a car is driven 200 km west and then 80 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

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You must draw a sketch to be able to do this problem. You also need to be familiar with the angles on a compass. This will result in you having a triangle : I can try and describe what it will look like:

The car travels due west for 200km. On your paper draw a horizontal line from point A to point B which is to the left of A. Mark off some distance which is to represent 200km. Now draw a second line to represent the 80km south west of line AB. This will be at an angle of 135° to the original line. Mark this point C. Now the displacement is represented by the line CA. Calculate this length by cos rule

b² = a² + c² -2ac Cos B

b² = 80²+200² -2*80*200*Cos 135

b² = 6400 + 40 000 - 22627.4

b² = 69 027.4

b = 262.73m

What is the direction?Calculate angle A by sin rule

a/sinA = c/sinC

sinA = (a*sinC)/c

sin A = 0.2153

A = 12.43° The angle between the 200km direction and the displacement direction is 12.43°

• Look at a map.

Draw your diagram; West is 180d, Soutwest is 45d more than if you took a turn to South.

Do you follow me so far? What's your angle between your lengths of 200 and 80? What is the total of all angles in a triangle? Your remaining angles total 45d.

Your answer will be more than 200 and less than 280 for the third side. I do not know how to go any further, but I suspect that it is less than 264. Let me know.

• Anonymous