In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __, BC = __ Case 2 : B∈NC, AB = __, BC = __ Case 3 : C∈BN, AB = __, BC = __

Case 1:

Case 2:

Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

This gives:

Take square roots of both sides

To calculate BC, we consider ANC, where:

Collect like terms

Take square roots

So:

Case 2:

Using Pythagoras theorem in ANB, we have:

This gives:

Collect like terms

Take square roots of both sides

To calculate BC, we consider ABC, where:

Collect like terms

Take square roots

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

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