Question

PLEASE HELP ME THIS IS THE ONLY THING I DONT GET!!!The map connects cities X, Y, and Z. The highways connecting the cities make a right triangle Leo drove from city Y to city Z and Samantha drove from city Y to city X and then from city X to city Z. How many more kilometers did Samantha drive than Leo? Using complete sentences, justify your answer

Answer 1

Might as well use Pythagoras' theorem to get that missing side.

Answer 2

All right, so, we know that for a right triangle, we have that:
\[
a^2+b^2=c^2
\]Where \(a,b\) are the sides which are not the hypotenuse, while \(c\) is itself the hypotenuse.
We solve for \(b\) to get:
\[
b^2=c^2-a^2\implies
b=\sqrt{c^2-a^2}
\]So, we simply plug in the numbers to find the third side.
After that, we can simply compare the paths, to find out how much longer is the path across the two legs, rather than the hypotenuse.

Answer 3

16^2 + x^2 = 34^2

Answer 4

okay so then i will see who drove further??
when i ssolve it

Answer 5

yea exactly.

Answer 6

ok ok thanks sooo much but how would i type my ressponse?

Answer 7

is the missing side 30?

Answer 8

256 + x^2 = 1156
-256 -256
x^2 = 900
\[\sqrt{900}\]

Answer 9

figure that out and you get it your answer.

Answer 10

soooo i got 30 that correct, right?

Answer 11

and yea its 30.

Answer 12

ok and for my resoonse ill just type out the steps i did to prove that my awnsers right?

Answer 13

yea sure.

Answer 14

alright thankssss