Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 27

Pythagorean Theorem: Finding the Length of a Side of a Triangle

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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. Carpenters use this formula, called the Pythagorean theorem, to find needed measurements.

Terms, Symbols, & Abbreviations
right triangle-a triangle with one right (90-degree) angle
hypotenuse - the side of a right triangle that is opposite the right angle
altitude - the vertical side of a triangle
base - the bottom of a triangle
Pythagorean theorem - in a right triangle, the hypotenuse squared = sum of squares of other sides

Practice Exercise

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Find the length of the base (b) of the triangle when the altitude (a) is 5 and the hypotenuse (c) is 11.

Step 1 The formula is a2 + b2 = c2.
Step 2 Insert the known values.
52 + b2 = 112
Step 3 25 + b2 = 121
Step 4 b2 = 121-25
Step 5 b2 = 96
Step 6 b =<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007822702x/249183/27_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>

Problem Exercises

1.
Find the length of side b when side a is 6 and c is 12.
A)10.3923
B)108
C)13.4164
D)36
2.
Find the length of a when b is 7 and c is 13.
A)5.4772
B)10.9545
C)21.9089
D)27.3861
3.
Find the length of b when a is 12 and c is 17.
A)36.1248
B)24.0832
C)18.0624
D)12.0416
4.
Find the length of b, one side of a corner bracket, when a is 4'' and c is 5''.
A)6''
B)5''
C)4''
D)3''
5.
Find the length of a, one side of a drywall piece for a ceiling overhang, when b is 12'' and c is 15''.
A)3''
B)5''
C)7''
D)9''
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