A smaller commuter airline flies to three cities whose locations form the vertices of a right triangle. The totaly flight distance (from city A to city B to city C and back to city A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. What are the other two distances between the cities?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

A smaller commuter airline flies to three cities whose locations form the vertices of a right triangle. The totaly flight distance (from city A to city B to city C and back to city A) is 1400 miles. It is 600 miles between the two cities that are furthest apart. What are the other two distances between the cities?

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

This requires use of the pythagorean theorem (a^2 + b^2 = c^2). I'll define the distance between cities A and B as a, the distance between cities B and C as b, and the distance between A and C as c. We find that c is the hypotenuse of this triangle if it has the greatest distance (600 miles). a^2 + b^2 = 600^2 a^2 + b^2 = 360000 We have an issue here. We don't have the distances a and b. To find that, we use the fact that a + b + c = 1400 miles given in the problem. Since c = 600, a + b = 800. Solve for b = 800 - a. Use this as b in the pythagorean theorem. a^2 + (800 - a)^2 = 360000 a^2 + (800 - a)(800 - a) = 360000 a^2 + 640000 - 1600a + a^2 = 360000 2a^2 - 1600a + 280000 = 0 a^2 - 800a + 140000 = 0 a^2 - 800a = -140000 a^2 - 800a + 160000 = 20000 (completing the square, we take -800/2 = -400 and square that to get 160000; then we add it to both sides) (a - 400)^2 = 20000 a - 400 = 100sqrt(2) a = 400 + 100sqrt(2) = 541 miles b = 800 - (400 + 100sqrt(2)) = 400 - 100sqrt(2) b = 259 miles
well, whats the distance from city C to city A then? O.o
That is the 600 miles given in the problem.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

But on the picture it says the 600 miles is from City A to City B O_O
Oh, I'm sorry. I don't have a picture to look at, so I just chose the 600 miles to be from city C to city A. It can be from city A to city B if that's what the picture says. The 541 miles and 259 miles just represent the other two distances. You'll have to put them where they fit.
Well that makes sense. Thank you so much!

Not the answer you are looking for?

Search for more explanations.

Ask your own question