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Look at image
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Look at image And help please-example-1

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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.

User David Oneill
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