Carpentry & Building Construction © 2004

Pythagorean Theorem: Finding the Hypotenuse of a Right Triangle

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Carpenters must make sure that walls and floors are square as they work. In this sense, square means that the parts are at right angles to each other.

As shown in the figure, a diagonal line drawn on a rectangular surface divides the surface into two triangles. If the sides of the rectangle are truly at right angles to each other, then both triangles will be right triangles. The Pythagorean theorem can be used to determine whether the triangles are right triangles.

The Pythagorean theorem states that in a right triangle, the hypotenuse squared equals the sum of the squares of the two remaining sides. The hypotenuse is the side opposite the right angle. The formula is a2 + b2 = c2, where a is the altitude, b is the base, and c is the hypotenuse.

A simplified equation is c =  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/26_1.GIF','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>

Practice Exercise

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/26_2.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>

Find the diagonal of a wall that is 9' high and 19' long.

Step 1		The formula is c =	<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/26_1.GIF','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>
Step 2		Insert the known values.

		c =	<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/26_2.GIF','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>
Step 3		c =	<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/26_3.GIF','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>
Step 4		c =	<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/26_4.GIF','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>

Problem Exercises

1.		Find the diagonal of a floor that is 12' long and 14' wide.
			A)	9.2195'
			B)	18.4391'
			C)	27.6586'
			D)	36.8781'
2.		Find the diagonal of a wall that is 8' high and 11' long.
			A)	13.6015'
			B)	27.2029'
			C)	40.8044'
			D)	54.4058'
3.		If a floor is 15' × 22', then the diagonal is
			A)	13.3135'.
			B)	19.9703'.
			C)	26.6271'.
			D)	53.2540'.
4.		If a wall measures 10' × 18', then the diagonal is
			A)	10.2956'.
			B)	20.5913'.
			C)	30.8869'.
			D)	41.1825'.
5.		The floor on a 20' × 24' addition has a diagonal measuring
			A)	7.8102'.
			B)	15.6205'.
			C)	23.4307'.
			D)	31.2410'.