Math Question: Distance Between Supermarket & Smoothie Store

[daniel4]

Ok, here is the question, please don't laugh, I am not great at maths

here is is:

The Bread shop is 655 metres from the Smoothie Store, 393 Metres from the pie shop, and 314 metres from the Supermarket. The pie shop is 236 metres from the Supermarket and 524 metres from the Smoothie Store.

Assuming the distance between the Supermarket and the Smoothie Store is less than the distance between the Bread shop and the Smoothie Store, what is the distance between the Supermarket and the Smoothie Store? Please round to the nearest metre.

I would really appreciate a solution soon. Thanks!:D

I know I have not provided working I have done, but I have wrote this all down on paper and tried to work it out and I cant:( Then, I figured it is probably trigonometry which I am not very good at, at all.

Edit: I think its trigonometry - which I am not very good at:( Just involves the simple formula - would love some help. thanks!

 

[daniel4]

Btw, I think this is a trigonometry question.

 

[JesseM]

In this type of problem it helps to draw a diagram. You have two triangles here--one whose corners are the bread shop, the pie shop and the supermarket, and the other whose corners are the bread shop, the pie shop and the smoothie store. You know the lengths of all three sides of both triangles, and they both share a common base, the line segment from the bread shop to the pie shop. What I'd recommend is imagining you're plotting all these points on an x-y graph, with the base of the triangles as a horizontal line along the x-axis--if the bread shop is at the origin (x=0, y=0), then the pie shop would be at (x=393, y=0). Then if you can figure out the x and y coordinates of the remaining two points (the supermarket and the smoothie shop), you can use the pythagorean theorem to figure out the distance between them.

Now, it could be that one point is above the x-axis and one is below, but they give you the clue that "the distance between the Supermarket and the Smoothie Store is less than the distance between the Bread shop and the Smoothie Store", so as a starting assumption I'd imagine they were both above the x-axis. Since you know the lengths of all the sides of each triangle, you can use the http://www.ucl.ac.uk/Mathematics/geomath/trignb/trig12.html to figure out the cosine of the angle of each corner, and then use the cos^-1 button on a calculator to find the angle of each corner. Then you can figure out the x and y coordinates of the supermarket by looking at the right triangle with the line between the bread shop and the supermarket as the hypotenuse, another side along the x-axis whose length is equal to the x-coordinate of the supermarket, and a third side parallel to the y-axis whose height is equal to the y-coordinate of the supermarket (a bit confusing when written, but try drawing it and hopefully you'll see what I mean). To find the lengths of these sides, use the rule that the sine of an angle is equal to the opposite side over the hypotenuse, and the cosine of an angle is equal to the adjacent side over the hypotenuse (see the diagram http://id.mind.net/~zona/mmts/trigonometryRealms/introduction/rightTriangle/trigRightTriangle.html ). Then you can get the x and y coordinates of the supermarket, and do the same for the smoothie store, and use the pythagorean theorem $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }$$ to find the distance between them. Make sure the distance is less than the distance between the bread shop and the smoothie store, if it isn't you may need to reorient the positions of the supermarket and the smoothie store (make the x and/or y coordinate of one of them into a negative number, although the absolute value won't change, and recalculate the distance).

 

[daniel4]

Whoah..didnt expect such a large answer:D Thanks. Ill try it out and reply here if I still can't get it..lol.

 

[daniel4]

I am finding this really confusing:( I tried drawing the triangles, and the x-y graph, but I am getting all confused with myself. Thanks for helping, I don't think I am going to get the answer to this question though.

It would be better (I fine if you don't want to do this) if you could explain exactly how you did it step by step with the answer you got along the way..That way i would have the answer and understand how you did it:) Then, next time I would be able to do it myself.

 

[JesseM]

I am finding this really confusing:( I tried drawing the triangles, and the x-y graph, but I am getting all confused with myself. Thanks for helping, I don't think I am going to get the answer to this question though.

It would be better (I fine if you don't want to do this) if you could explain exactly how you did it step by step with the answer you got along the way..That way i would have the answer and understand how you did it:) Then, next time I would be able to do it myself.

Would you be able to show which step you got stuck on, and if possible show what you tried to do there and why it didn't work or what got you confused? I think you'd be more likely to remember this way than if I just gave you a complete walkthrough.

 

[daniel4]

Thanks so much for the help:) I have figured it out - and checked over it twice to confirm my answer. I can't believe you provide all this support for free!