Question

In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.

Answer 1

Ab is 30 and BC is 50
See the attachment.
Hope this helps

Answer 2

The length of the BC is 50 inches and the length of AB is 30 inches.

What is the Pythagoras theorem?

The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angle triangle.

Since AN is an altitude, this means that it is perpendicular to BC.  

This means BN and AN are the legs of one right triangle, with AB being the hypotenuse:

$\rm 18^2+24^2 = AB^2\\\\324 + 576 = AB^2\\\\900 = AB\\\\900}= AB^2\\\\AB^2=30^2\\\\ AB =30$

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

$\rm 24^2+NC^2 = 40^2\\\\576 + NC^2 = 1600\\\\576 + NC² - 576 = 1600 - 576\\\\NC^2 = 1024\\\\NC^2=32^2\\\\NC=32$

The length of BC is;

$\rm BC = BN + NC = 18 + 32 = 50$

Hence, the length of the BC is 50 inches and the length of AB is 30 inches.

To know more about the Pythagoras theorem click the link given below.

https://brainly.com/question/9802011

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