Answer:
c = √61
Explanation:
Determining the lengths of a (aka BC) and b (CA) using the distance formula:
- Before we can determine the length of c (BA) using the Pythagorean Theorem, we need to determine the lengths of a (aka BC) and b (aka CA) using the distance formula.
The distance formula is given by:
d = √[(y2 - y1)^2 + (x2 - x1)^2], where
- d is the distance,
- (x1, y1) is one point,
- and (x2, y2) is another point.
Finding the length of a (aka BC):
Since the distance formula requires us to have two sets of coordinates, we can find the distance, d, between points B and C (i.e., the length of a, aka BC) by substituting the coordinates of B for (x1, y1) and the coordinates of C for (x2, y2) in the distance formula:
B(2, 8), C(2, ,3)
d = √[(3 - 8)^2 + (2 - 2)^2]
d = √[(-5)^2 + (0)^2]
d = √[25]
d = 5
Thus, the length of a (aka BC) is 5 units.
Finding the length of b (aka CA):
We can now find the distance, d, between points C and A (i.e., the length of b, aka CA) by substituting the coordinates of C for (x1, y1) and A (8, 3) for (x2, y2) in the distance formula:
A (8, 3)
d = √[(3 - 3)^2 + (8 - 2)^2]
d = √[(0)^2 + (6)^2]
d = √[36]
d = 6
Thus, the length of b (aka CA) is 6 units.
Finding the length of c (aka BA):
Now we can find the length of c (aka BA) by substituting 5 for a and 6 for b in the Pythagorean Theorem:
a^2 + b^2 = c^2
5^2 + 6^2 = c^2
25 + 36 = c^2
√61 = √c^2
√61 = c
Thus, the length of c (aka BA) is √61 units.