math help plz?

Question

The car shop is 655 meters from the Smoothie Store, 393 Meters from the library, and 314 meters from the Parlour. The library is 236 meters from the Parlour and 524 metres from the Smoothie Store.

Assuming the distance between the Parlour and the Smoothie Store is less than the distance between the car shop and the Smoothie Store, what is the distance between the Parlour and the Smoothie Store? Please round to the nearest meter!!


{{{this makes like no sense to me can you help plz.}}}

Answer 1

ok
u have a triangle formed by the Car Shop (CS), the Smoothie Store (SS) and the Library
let's check if this triangle fits Pythagore's theory:
distance CS to L = a =393 m
distance L to SS = b = 524 m
distance CS to SS = c = 655 m

let's check if a^2 + b^2 = c^2
a^2 + b^2 = 429025
c^2 = 429025
therefore we have a right triangle with a 90 degree angles at the Library

now the 2nd triangle formed is between CS the parlour (P) and SS
dist. CS to P = e = 314m
dist. P to SS = d = ?
dist L to P = f = 236m
also checking if there's a right triangle in the space CS-L-P
e^2 + f^2 = 154292
a^2 = 154449
ok it's not a 90 degree angle 100% but it can be considered as one the distances are large and this is negligeable
angle (L-CS-SS) = x
cos x = a/c => cos x=393/655 => x=53.13
angle (L-CS-P) = y
cos y = e/a => cos y = 314/393 => y = 36.97
angle (P-CS-SS) = z
z = x-y = 16.16
let h be the altitude in triangle CS-P-SS
h forms a right angle on SS cutting SS into point A
in right traingleCS-A-P
sin z = h/e => h = e*sinz=314 * sin(16.16)
h= 87.39 m
and cos z= (dist.CS-A)/e => CS-A=e*cosz= 301.59 m
so A-SS = 655-301.59 = 353.41 m
in right triangle P-A-SS
d^2 + h^2 = (A-SS)^2
d^2 = (353.41)^2 - (87.39)^2 => d = 342.43m

Answer 2

I'm thinking the car shop and the smoothie store are the farthest apart. then the library is a little closer and the parlour is even closer to the car shop. since from the library to the smoothie store is 524, they can't be in a straight line with the parlour and car shop, or that would give more then the distance from the car shop to the smoothie store, so I'm thinking the library is somewhere to the side and the car shop and parlour and smoothie store are in a line. first car shop, then parlour, then smoothie store. subtract 314 (distance of parlour from car shop) and you get 341. that's the best I can think of.

Answer 3

4 points ABCD are in the plane and AB=655, AC=393, AD=314, CD=236 and CB= 524. In other words you have the dimensions for ABC and ACD. So you have 2 triangles with a common side. That leaves 4 possibilities for their mutual position. B and D can be on the same side of AC on one hand or not, and can be on the same side of the bisector of BD or not. You know that BD

Answer 4

524 - 236 = 288 meters

The parlour is between the library and the smoothie store.

Answer 5

629 meters, what u do is u add the distance from the library to the parlour and then add the distance from the library to the smoothie store.

Answer 6

969 meters. from parlour go to the car shop and then to the smoothie store

Answer 7

Table of solution:
; ; ;C.S ; S.S ; Lib. ; Par.
C.S ; 1 ; 655 ; 393 ; 314
S.S ; 655 ; 1 ; 524 ; ?
Lib. ; 393 ; 524 ; 1 ; 236
Par ; 314 ; ? ; 236 ; 1


?= calculate ?< 655

Answer 8

939 meter

Answer 9

Honestly now, if you can't do the Lenny Conundrum, just wait for one you can do. Or go to the Neopets boards, people tend to post the answer there.

Answer 10

Um.. E=Mc Squared?????