an airpalne files 400km from the city A to city B?

Question

an airplane flies 400 km west from city A to city B,then 300km northwest to city C and finally 100km north to city D. how far it is from city A to city D? in what direction must the airplane head to return directly to city A from city D?

Answer 1

first leg is 400 - base +
third leg is 100 north +

so we need to find what those additional distances are
what we have is an isosoles right triangle -
300 ^2 = 2( side ^2)
90,000 = 2 (x^2)
45,000 = x^ 2...... so you have to find the square root of 45,000

or may be not - we still have a right triangle -

so our solution to distance

(400^2 + 45000) plus (100^2 + 45000) = (hypotenuse ^2) distance a-d
160,000 + 45,000 + 10,000 + 45,000 = 260,000= hypo^2

the square root of 260,000 is your distance (you do the math)

direction will be "east south east"

due east is the opposite of due west
south east is the opposite of north west

in between them is east south east

Answer 2

Try drawing a picture.