Can anyone figure out this problem?

Question

Store A is 655 metres from the Store B, 393 Metres from the Store C, and 314 metres from Store D. Store C is 236 metres from the Store D and 524 metres from Store B.

Assuming the distance between Store D and Store B is less than the distance between Store A and the Store C, what is the distance between the Store D and Store B? Please round to the nearest metre.

Answer 1

This is a difficult problem to describe without showing you on a piece of paper, but I'll try help you visualize how to solve it. I'm assuming this is a class in which you have learned about sin, cos, tan arcsin, arccos and arctan.

Get a large piece of paper and it would sure help if you had a ruler and a protractor. Make a dot in the very center of the piece of paper and label it "A" for store A.

Using the protractor set to about 6.5 cm (or inches) - (to represent 655 meters) draw a circle centered at point A and label the circle "B". Store B is somewhere on that circle.
Using the protractor set to about 3.9 cm (or inches), (to represent 393 meters) draw another circle centered on point A and label the circle "C". Store C is somewhere on that circle.
Using the protractor set to about 3.1 cm (or inches), (to represent 314 meters) draw another circle centered on point A and label the circle "D". Store D is somewhere on that circle.

Now, pick any point on circle C and call that Store C. Using the protractor set to 2.3 cm (or inches) place the point of the protractor on Store C and mark an intersection with circle D. You will have two intersections and Store D will be located at one of those intersections. Pick one and label it Store D.
Finally, with the protractor set to 5.2 cm (or inches) place the point of the protractor on Store C and mark an intersection with circle B. You will have two intersections and Store B will be located at one of those intersections. Pick one and label it "B"

Now, draw a line from A to C and label it 393 meters
Draw a line from A to B and label it 655 meters
Draw a line from C to B and label it 524 meters.

This forms a triangle and it should look pretty close to being a right triangle. To check to see if it is take the square root of 393^2 + 524^2 and you'll find it = 655. Yes, it's a right angle.
Calculate the angles in this triangle using arcsin, arccos or arctan.

We haven't marked where Store D is yet but there are two possible points marked on its circle. The problem says that the distance from D to B is less than the distance from A to C. Using that information, figure out which of the two intersection marks are Store D and label it "D".
Now draw a line between points A and D, points C and D, points B and D.

You will now have more triangles. You can solve this problem by calculating the angles in these triangles and use this information to eventually find the distance between Stores D and B by solving the angles and legs of the triangles. You may have to sum the angles of two adjoining triangles to get the angle in a different triangle.

The important thing in solving this problem is to be able to visualize it. Drawing it on paper helps. It's not a simple problem but give it a try.

Answer 2

Are they in a straight line, or circle, or square or rectangle or triangle or some other pattern?

Answer 3

is there a certain pattern involved, i.e square, circle??