12 replies to this topic

[Debasis]

Spoiler for I verified my calculations...

...and sqrt(37) is the correct distance between the towns. For any a and b, where a is the distance from the car to Alpha and b is the distance from the car to Beta, the maximum distance from the car to Gamma is a+b and is achieved when the angle formed by the lines connecting the car with Alpha and Beta is equal 120 degrees. Applying the law of cosines with 120 degree angle we get the distance between towns = sqrt( 3² + 4² - 2 * 3 * 4 * cos(pi/3) ) = sqrt(37).

three towns.png

hey man can you tell me how you worked out that the angle between alpha and beta should be 120 degrees .i just acant understand..Thanks

[k-man]

 

Spoiler for I verified my calculations...

...and sqrt(37) is the correct distance between the towns. For any a and b, where a is the distance from the car to Alpha and b is the distance from the car to Beta, the maximum distance from the car to Gamma is a+b and is achieved when the angle formed by the lines connecting the car with Alpha and Beta is equal 120 degrees. Applying the law of cosines with 120 degree angle we get the distance between towns = sqrt( 3² + 4² - 2 * 3 * 4 * cos(pi/3) ) = sqrt(37).

three towns.png

hey man can you tell me how you worked out that the angle between alpha and beta should be 120 degrees .i just acant understand..Thanks

I knew someone would ask that question

 

It was a little messy and maybe not in the most efficient way, but...

Spoiler for

I used the laws of cosines and sines to express the distance to Gamma as a function of the angle between Alpha and Beta. Then I to took a derivative of that function to find the local maxima and found it to be at 120 degrees. If I have more time later, I may post the complete solution

[Debasis]

 

Spoiler for I verified my calculations...

...and sqrt(37) is the correct distance between the towns. For any a and b, where a is the distance from the car to Alpha and b is the distance from the car to Beta, the maximum distance from the car to Gamma is a+b and is achieved when the angle formed by the lines connecting the car with Alpha and Beta is equal 120 degrees. Applying the law of cosines with 120 degree angle we get the distance between towns = sqrt( 3² + 4² - 2 * 3 * 4 * cos(pi/3) ) = sqrt(37).

three towns.png

hey man can you tell me how you worked out that the angle between alpha and beta should be 120 degrees .i just acant understand..Thanks

I knew someone would ask that question

 

It was a little messy and maybe not in the most efficient way, but...

Spoiler for

I used the laws of cosines and sines to express the distance to Gamma as a function of the angle between Alpha and Beta. Then I to took a derivative of that function to find the local maxima and found it to be at 120 degrees. If I have more time later, I may post the complete solution

thanks!