The units of the subway map below are in miles. Suppose the routes between stations are straight. Station F, not shown on the map, is 12 miles west and 3 miles north of Station A. What is the approximate distance between Station E and Station F?

Question

The units of the subway map below are in miles. Suppose the routes between stations are straight. Station F, not shown on the map, is 12 miles west and 3 miles north of Station A. What is the approximate distance between Station E and Station F?

The distance from Station E to Station F is approximately __ miles.
(Round to the nearest tenth as needed.)

Answer 1

No map, so no data on E.

Answer 2

To find the approximate distance between Station E and Station F, we can use the Pythagorean theorem.

The distance is given by the equation:

distance = √((change in x)^2 + (change in y)^2)

In this case, the change in x is 12 miles (since Station F is 12 miles west of Station A) and the change in y is 3 miles (since Station F is 3 miles north of Station A).

Using the Pythagorean theorem, we have:

distance = √((12^2) + (3^2))
distance = √(144 + 9)
distance = √153
distance ≈ 12.37 miles

So, the approximate distance between Station E and Station F is approximately 12.4 miles.

Answer 3

To find the approximate distance between Station E and Station F, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the straight distance between Station F and Station A forms the hypotenuse of a right triangle, with the distance west being the length of one side (12 miles) and the distance north being the length of the other side (3 miles).

To find the length of the hypotenuse (distance between Station E and Station F), we can apply the Pythagorean theorem:

c^2 = a^2 + b^2

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

So, in this case:

c^2 = 12^2 + 3^2
c^2 = 144 + 9
c^2 = 153

To find the value of c (the distance between Station E and Station F), we take the square root of both sides:

c = √153

Using a calculator or a math tool, we can find:

c ≈ 12.4

Therefore, the approximate distance between Station E and Station F is approximately 12.4 miles.

The units of the subway map below are in miles. Suppose the routes between stations are straight. Station​ F, not shown on the​ map, is 12 miles west and 3 miles north of Station A. What is the approximate distance between Station E and Station​ F?

No map, so no data on E.

To find the approximate distance between Station E and Station F, we can use the Pythagorean theorem.

The units of the subway map below are in miles. Suppose the routes between stations are straight. Station F, not shown on the map, is 12 miles west and 3 miles north of Station A. What is the approximate distance between Station E and Station F?