Question

An airplane flies 200 km east from City A to City B, then 200 km south from city B to city C and finally 100 km northwest to city D. How far is it from city A to city D? In what direction must the airplane head to return directly to city A from city D?

Answer 1

Is this a multiple choice question? if so can you give me the answer choices? if its not, Im working on the answer for this one :)

Answer 2

its not multiple choice .. its a problem solving .

Answer 3

Alright, Im not sure if I'll be much help, but I think the answer to is Use pythagorean theorem h= the square toot of 200^2 + 200^2. = 282.84Km. then substract 100km = 182.84 direction: To return from city d to city a it has to keep going west of north. or Northwest, since its a 45 angle.

Answer 4

so I think the answer is 100. but you might want to check my work and make sure I didn't make any errors.

Answer 5

I think that graph below describes your situation, please:

do you agree?

Answer 6

@acsahmanuel26

Answer 7

thank you so much :D

Answer 8

what is the length of segment AB?

Answer 9

sorry, what is the length of segment AC?

Answer 10

no, sorry, it is half diagonal of the square whose side is 200 km, namely:

Answer 11

so I have to apply theorem of Pitagora, namely:
\[AC=\sqrt{200^{2}+200^{2}}=200*1.41=282 km\]
do you agree?

Answer 12

@acsahmanuel26 do you know theorem of Pitagora?

Answer 13

yeah c2=a2+b2

Answer 14

ok! so AC=282 km, do you agree?

Answer 15

is the distance from segment ac is 282.84?

Answer 16

that's right!

Answer 17

thank you.. so the distance from city a to city d is 282.84 km?

Answer 18

now please note that:

Answer 19

182 km?

Answer 20

no, please note my drawing, you are at D and DC=100 km. Now you know thatAC=282 km, so we can write:
\[x+100=282.84\]
where x =distance AD, so?

Answer 21

then x=282.82-100=...

Answer 22

x=182 km,
you are right!
congratulations!

Answer 23

thank you so much... and the direction is northwest?

Answer 24

that's right!