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Home > Measurement > Pythagoras Theorem > Finding a short side

Finding a short side

Pythagoras theorem can be used in finding a short side’s dimension when the lengths of the hypotenuse and the other side are known.

Example 1 : Find the length of the side marked with the pro-numeral.

k2  +  52  =  13finding a short side_1

k2  =  132  –  52

k  =  sqrt{169~-~25}

=  sqrt{144}

=  12 mm

 

Example 2 : What is the length of `k` (one of the short sides) in this triangle

k2  +  122  =  212  finding a short side_2

k2  =  212  –  122

k  =  sqrt{441~-~144}

=  sqrt{297}

=  17.2 m (to 1 decimal place)

 

Example 3 : Find the length of the short side ‘d’ in this triangle. Express the answer as a surdfinding a short side_3

d2  +  62  =  172

d2  =  172  –  62

d  =  sqrt{289~-~36}

=  sqrt{253}

 

Example 4 : Find the length of the third side, correct to one decimal place, if the length of the hypotenuse and a shorter side are 7.4 cm and 3.2 cm respectively.

a2  +  b2  =  c2

(3.2)2  +  b2  =  (7.4)2

b2  =  7.42  –  3.22

b  =  sqrt{54.76~-~10.24}

=  sqrt{44.52}

=  6.7 cm