puzzle / math question ?

Question

petco is 655 metres from walmart , 393 metres from dominos , and 314 metres from bestbuy .

dominos is 236 metres from bestbuy and 524 metres from walmart

how far is bestbuy from walmart ?


can you plz explain how you come to ur answer too :)

Answer 1

Let Petco be P, Walmart be W, and so on.
Assuming all pts. P, W, ... are co-planar.
using cosine rule,
cos(WDP) = (524^2+393^2-655^2)/(2*524*393)
= 0
So WDP = 90 deg,
cos(PDB) = (393^2+236^2-314^2)/(2*393*236)
= 0.601355
sin(PDB) = 0.79898
So,
ang(BDW)=90+ang(PDB)...1
or ang(BDW)=90-ang(PDB)....2
Case 1 yields;
BW^2 = 524^2+236^2+2*524*236*0.79898
BW = 726.555 m
Case 2 yields;
BW^2 = 524^2+236^2-2*524*236*0.79898
BW = 364.228 m

Answer 2

The figures that I am giving are rough estimates and are close to the correct answer.

The best buy is either 943 meters or 483 meters from best buy.

How?

Simply put petco at the center.

Now draw a circle of radious 655 with the center being at petco. This circle lets say Circle W is the line along which somewhere is the location of walmart.

Now draw a circle of radious 393 with petco as center for the probable location of Dominos and call it Circle D. This is where dominos is.

Now draw a circle of radious 314 with petco as center and call it Circle B. This is the line on which best buy is.

Choose a random point on Circle D and lets assume that this is dominos.

From dominos location draw a circle of 236 radious. This will intersect the Circle B at two points. Lets call these points, B1 and B2. These are the only two possible points where bestbuy could be located.

From dominos again location draw a circle of 524 radius. This will intersect the circle W at two points. Lets call these new poits as W1 and W2. These are the only two possibilities where wlamart can be located.

Rest is simple. Draw a line from B1 to W1 and measure and then draw a line from B1 to W2 and measure. Results from B2 to W2 and W1 will be similar.

Tis is how I ot to the answer. There must be a more simple acurate way of doing it, but it will also mean much complex calculus or something like that.

Answer 3

Here's a picture

math to follow

http://usera.imagecave.com/antsam999/Math1.jpg

You see, there's a big triangle, made up of 3 smaller triangles, we simply need to find the missing side. We have more than enough information to do so.

First, the sum of the internal angles of ANY TRIANGLE =180 degrees

so the sum of the angles of BB-Petco-Walmart triangle=180

therefore, A+B+C=180 (where A, B, C are angles at the points of the stores)

using the sine rule
http://www.teacherschoice.com.au/Maths_Library/Trigonometry/solve_2.gif

an the cosine rule
3. The cosine rules

a² = b² + c² - 2bc cosA

or

b² = a² + c² - 2ac cosB

or

c² = b² + a² - 2ba cosC


we can solve this problem.

first, we need to fin the angles. Since we have 3 sides of the other 2 triangles, you can process to find all the angles using the Cosine rule.

concentrate on the petco, walmart, dom triangle first, find all these angles, then the next triangle that we know (bb, D, P) then you'll have the angles and will have enough info to find the last triangle's sides and angles.

http://usera.imagecave.com/antsam999/Math2.jpg

A^2=B^2+C^2-2BC*Cos a
Cos a = B^2+C^2-A^2/(2BC)
Cos a = 274549+154449-429025/42444
Cos a = 0/42444 = 0 Cos a = 0 = 90 °

So the angle between Walmart-ominos-Petco is 90 °

Repeat on Angle B, then use the sine rule (180-Angle A - Anble B=Angle C) to find all the angles. Repeat these steps on the next triangle, then you'll have 2 of the 3 angles around Petco. Subtract these 2 angles from 180, and you'll have the last angle, which you can use to solve the triangle.

hERE'S THE SOLUTION, YOUC AN FIGUER IT OUT FOR YOURSELF, IT'S A ROUGH
http://usera.imagecave.com/antsam999/SOLVE.jpg

Answer 4

There are 2 answers to the given conditions. Its hard to visualise until you mark the radii on paper and it will not be possible to show the drawing here.
Hence working backwards: petco(P), dominos(D) and walmart(W) actually form a right-angle triangle because ratio of their distances is 5:4:3. Angle PDW =90degrees
bestbuy (B) can lie within or without this triangle because there are 2 possible locations which satisfy 314m from P and 236m from D. Assuming B lies within the triangle, its distance from W is 481m. I have not done the calculations for the other condition.
just use the equation:
a^2 = b^2 + c^2 -2bc cos(angle a)

Answer 5

The distance between Bestbuy and Walmart is: 726∙55....meters.

Draw a diagram out, mark in the numbers. You have two triangles together. Extend the lines of two of the sides to make a third triangle and work out the angles and distances.
By using the Sine formula and the Cosine formula a number of times the answer may be calculated.
a² = b² + c² - 2bc cosA
a/SinA = b/SinB = c/SinC

Answer 6

It only works if there are straight roads between towns. make a line dominos----walmart(5.24) then make a circle with center walmart with radius of 6.55sm.This circle will show u where petko is.Use same line dominos----walmart and make the same with the diminos but use radius 3.93sm. The two circles will cross two times - the poslible oportunities where petko is. u have now three points and u know the distancesses between them u can find easily where is the town. I cant give u the answer sorry because i draw it on hand and its not correct. try this it can help

Answer 7

341 mt
if petco is 655 mt from walmart and 314 mt from best buy
check the difference

Answer 8

bestbuy is 760 metres from walmart because if you add 524 and 236 it makes 760

Answer 9

a million) purely detect the kit... pudding= x and Swiss rolls = y 5x + 4y = 40 5 2x + 6y = 51... as we ought to choose to understand the fee of y purely multiply the 1st equation via -2 and the 2d via 5 and upload the equations; -10x -8y = -ninety 10x +30y = 255 at the same time with the two equation we get 22y = one hundred sixty five then y = one hundred sixty five/22 = 7.5 ok! 2) x the age of the mummy and y the age of the daughter. x = 3y x-6 = 5(y-6) ... as we ought to choose to understand the fee of y ... replace x = 3y indoors the 2d equation and get: 3y - 6 = 5(y-6) ==> 3y -6 = 5y - 30 ==> 2y = 24 ==> y = 12 ok!

Answer 10

341 mt
if petco is 655 mt from walmart and 314 mt from best buy
check the difference
341 mt walmart and best buy

petsco >>>>>>>>>314 B/buy >>>>>>>>655W/m
>>>>>>>>>>>>>>>>>>>>I<--341--mt