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In the ā–³ABC, the altitude AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Answer: Case 1 : Nāˆˆ BC . It is . If the case is possible, then AB = in, BC = in Case 2 : Bāˆˆ NC . It is . If the case is possible, then AB = in, BC = in Case 3 : Cāˆˆ BN . It is . If the case is possible, then AB = in, BC =

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Answer:AB = 30 in and BC = 50 in.

We use Pythagorean theorem to solve this. Ā Since AN is an altitude, this means that it is perpendicular to BC. Ā This means BN and AN are the legs of one right triangle, with AB being the hypotenuse:

18Ā²+24Ā² = ABĀ²

324 + 576 = ABĀ²

900 = ABĀ²

Take the square root of both sides:

āˆš900 =Ā āˆšABĀ²

30 = AB

NC and AN form the legs of the other right triangle, with AC being the hypotenuse:

24Ā²+NCĀ² = 40Ā²

576 + NCĀ² = 1600

Subtract 576 from both sides:

576 + NCĀ² - 576 = 1600 - 576

NCĀ² = 1024

Take the square root of both sides:

āˆšNCĀ² =Ā āˆš1024

NC = 32

BC = BN + NC = 18 + 32 = 50

Step-by-step explanation:

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