Wood Technology & Processes

Self-Check Math Quizzes : Self-Check Math Quizzes

Math Activity 9

Pythagorean Theorem: Finding the Hypotenuse of a Right Triangle


<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007894094x/300500/9_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"> (9.0K)</a>

Woodworkers must make sure that the sides, tops and bottoms of casework are square to each other during assembly. 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/007894094x/300500/a_sqaure.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>.

Terms, Symbols, & Abbreviations

right triangle—a triangle with one right (90-degree) angle
Pythagorean theorem—in a right triangle, the hypotenuse squared = sum of squares of other sides
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

Practice Exercise

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007894094x/300500/9_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 1The formula is c = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007894094x/300500/a_sqaure.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>
Step 2Insert the known values. c = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007894094x/300500/9_sqaure.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>
Step 3c = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007894094x/300500/81_square.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>
Step 4c = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/007894094x/300500/442_sqaure.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>
Step 5c = 21.0238'


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'.
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