Question

You walk east 720 feet to get from your house to class. After class, you walk southwest 1,044 feet to meet your friends for lunch. When walking the 756 feet back home from lunch, what direction are you traveling?

A.
N
B.
NE
C.
NW
D.
W

Answer 1

Answer: Option A. N

Solution

The three given sides form a triangle with sides 720, 756, and 1,044

The largest side is 1,044. We can use the Pythagoras Theorem to clasify the triangle comparing the square of the largest side with the sum of the square of the other two sides:

1,044^2 compared with 720^2+756^2

1,089,936 compared with 518,400+571,536

1,089,936 compared with 1,089,936

1,089,936 = 1,089,936

Beacuse of we get an equality, this is a right triangle and the angle between the smallest sides must be right: the angle between 720 and 756 must be 90°. These sides must be perpendiculars, and because of the side of 720 is horizontal (east), the side of 756 must be vertical (north).

Answer 2

The correct answer option is B. NE.

Explanation:

This makes a triangle with E-W leg 720 , then 45 degree angle to go South-West 1044 feet . While the angle to go 756 feet home is unknown.

So we need to find the angle between 1044 and 756 leg.

`(sin45)/(756) =  (sin x)/(720)`

`sin x = (509.12)/(756)`

`sin x=0.673`

`x= 42.3`°

The supplement of this angle is 180 - 42.3 = 137.67°

Therefore, the direction is 2.67 North to East.