Draw a diagram to solve this problem: Ajax is 8 km due west of Oshawa. Uxbridge is 6 km NW of Oshawa. How far is it from Ajax to Uxbridge? Explain whether you have enough information to solve this problem?
Draw the -8km vector from the origin on the neg. x-axis.
Draw the 6km vector from the origin 45o
west of north(135o).
Du = 6km @ 135o.
Du = 6*cos135 + i6*sin135
Du = -4.24 + i4.24 = Dist. from Oshawa
to Uxbridge.
Da = -8 km=Dist. from Oshawa to Ajax.
D = Du - Da
D = (-4.24+i4.24) - (-8)
D = 3.76 + i4.24
D^2 = (3.76)^2 + (4.24)^2 = 32.12
D = 5.67 km.
post it.
To solve this problem, we can draw a diagram using two points: Ajax and Uxbridge, along with Oshawa.
First, draw a point to represent Ajax. Label it "Ajax" and place it on the left side of your diagram.
Next, draw a point to represent Oshawa. Label it "Oshawa" and place it towards the center of your diagram.
Then, draw a point to represent Uxbridge. Label it "Uxbridge" and place it towards the top-right of your diagram.
Next, draw a line segment connecting Ajax and Oshawa, and label it with a distance of 8 km. This line should be horizontal, going from the "Ajax" point to the "Oshawa" point.
Then, draw a line segment connecting Oshawa and Uxbridge, and label it with a distance of 6 km. This line should point towards the top-right, forming a diagonal line.
Finally, draw a right triangle using the lines you've drawn. The horizontal line from Ajax to Oshawa represents the adjacent side, the vertical line from Oshawa to Uxbridge represents the opposite side, and the diagonal line from Ajax to Uxbridge represents the hypotenuse.
Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the two legs (adjacent and opposite), and c is the length of the hypotenuse, we can find the length of the line segment from Ajax to Uxbridge.
In this case, we have the length of the adjacent side (8 km) and the length of the opposite side (6 km). Plugging these values into the Pythagorean theorem, we get:
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
Taking the square root of both sides, we get:
c = 10 km
Therefore, the distance from Ajax to Uxbridge is 10 km.
So, the information provided is enough to solve the problem, and using the Pythagorean theorem and the diagram allows us to determine the distance between Ajax and Uxbridge.