# Question Video: Finding the Length of a Side in a Triangle Using the Right-Angled Triangle Altitude Theorem Mathematics

Find the length of the line segment π΄π·.

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### Video Transcript

Find the length of the line segment π΄π·.

To find the length π΄π·, we first note that π· is the projection of π΅ onto π΄πΆ and that the triangle π΄π΅πΆ is a right triangle at π΅. And now recalling the Euclidean theorem, this tells us that π΄π΅ squared is π΄π· multiplied by π΄πΆ. That is, the side length π΄π΅ squared is the product of the segment π΄π· with the length of the hypotenuse π΄πΆ. Weβre given that π΄π΅ is 34 centimeters and that the hypotenuse π΄πΆ is 40 centimeters. And substituting these values into the Euclidean theorem, this gives us 34 squared is π΄π· multiplied by 40. Dividing through by 40 and rearranging, this gives us π΄π· is 34 squared over 40, that is, 1156 divided by 40, which is 28.9. The line segment π΄π· is therefore 28.9 centimeters.