Town A lies 20 km north of town B. Town C lies 13 km west of town A. A small plane flies directly from town B to town C. What is the displacement of the plane.
Please explain how you got the answer
To find the displacement of the plane, we need to calculate the straight-line distance between town B and town C.
From the given information, we can create a triangle with town B, town A, and town C. The distance between town A and town B is 20 km, and the distance between town A and town C is 13 km.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the distance between town B and town C.
Let's label the distance between town B and town C as 'd':
d^2 = (20 km)^2 + (13 km)^2
d^2 = 400 km^2 + 169 km^2
d^2 = 569 km^2
Taking the square root of both sides, we get:
d ≈ 23.87 km
Therefore, the displacement of the plane is approximately 23.87 km.
To find the displacement of the plane, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this problem, we can create a right triangle with the distance between towns A and B as one of the sides (20 km) and the distance between towns C and A as the other side (13 km). The hypotenuse of this triangle will represent the displacement of the plane.
We can calculate the length of the hypotenuse using the formula:
hypotenuse = sqrt((side1)^2 + (side2)^2)
Plugging in the values:
hypotenuse = sqrt((20 km)^2 + (13 km)^2)
= sqrt(400 km^2 + 169 km^2)
= sqrt(569 km^2)
≈ 23.86 km
Therefore, the displacement of the plane is approximately 23.86 km.
Draw AB perpendicular to AC. Therefore, we have a right angle. Draw BC the hyp. of the rt. triangle formed.
The displacement is the straight-line distance from the starting point to the final point which is the hyp.
Disp. = hyp. = BC = Sqrt((AB)^2+(AC)^2).
AB = 20km.
AC = 13km.
BC = 23.9km = Disp.