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Length of arc AB, l = 21 cm Radius of pendulum, r = 75 cm Using we have <img class=Wirisformula style=vertical-align: -10px; src=/application/zrc/images/qvar/MAEN11034003-1.png alt=straight theta space equals space open parentheses 21 over 75 close parentheses to the power of straight c width=66 height=28 align=middle data-mathml=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msup»«mfenced»«mfrac»«mn»21«/mn»«mn»75«/mn»«/mfrac»«/mfenced»«mi mathvariant=¨normal¨»c«/mi»«/msup»«/math»> ∴ (a) <img class=Wirisformula style=vertical-align: -10px; src=/application/zrc/images/qvar/MAEN11034003-2.png alt=straight theta space equals space open parentheses 7 over 25 close parentheses to the power of straight c width=66 height=28 align=middle data-mathml=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msup»«mfenced»«mfrac»«mn»7«/mn»«mn»25«/mn»«/mfrac»«/mfenced»«mi mathvariant=¨normal¨»c«/mi»«/msup»«/math»> (b) <img class=Wirisformula style=vertical-align: -10px; src=/application/zrc/images/qvar/MAEN11034003-3.png alt=straight theta space equals space open parentheses 7 over 25 cross times 180 over straight pi close parentheses to the power of degree space equals space open parentheses 7 over 25 cross times 180 over 22 cross times 7 close parentheses to the power of degree equals open parentheses 882 over 55 close parentheses to the power of degree space equals 16 degree 2 apostrophe 11 apostrophe apostrophe width=375 height=30 align=middle data-mathml=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msup»«mfenced»«mrow»«mfrac»«mn»7«/mn»«mn»25«/mn»«/mfrac»«mo»§#215;«/mo»«mfrac»«mn»180«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mfrac»«/mrow»«/mfenced»«mo»§#176;«/mo»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«msup»«mfenced»«mrow»«mfrac»«mn»7«/mn»«mn»25«/mn»«/mfrac»«mo»§#215;«/mo»«mfrac»«mn»180«/mn»«mn»22«/mn»«/mfrac»«mo»§#215;«/mo»«mn»7«/mn»«/mrow»«/mfenced»«mo»§#176;«/mo»«/msup»«mo»=«/mo»«msup»«mfenced»«mfrac»«mn»882«/mn»«mn»55«/mn»«/mfrac»«/mfenced»«mo»§#176;«/mo»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mn»16«/mn»«mo»§#176;«/mo»«mn»2«/mn»«mo»`«/mo»«mn»11«/mn»«mo»`«/mo»«mo»`«/mo»«/math»>

Find the angle in (a) radians (b) degrees through which a pendulum swings if its length is 75 cm and its tip describes an arc of length 21 cm.

Length of arc AB, l = 21 cm

Radius of pendulum, r = 75 cm

Using $l over r space equals space straight theta comma$ we have $straight theta space equals space open parentheses 21 over 75 close parentheses to the power of straight c$

∴ (a) $straight theta space equals space open parentheses 7 over 25 close parentheses to the power of straight c$

(b) $straight theta space equals space open parentheses 7 over 25 cross times 180 over straight pi close parentheses to the power of degree space equals space open parentheses 7 over 25 cross times 180 over 22 cross times 7 close parentheses to the power of degree equals open parentheses 882 over 55 close parentheses to the power of degree space equals 16 degree 2 apostrophe 11 apostrophe apostrophe$

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