Solving problems using Pythagoras' theorem
Have a look at this example question, then try the question below.
A cable is attached, 30 metres above ground level, to a post.
The other end of the cable is 14 metres from the base of the post.
Regulations state that the cable must measure less than 35 metres.
Are the regulations being met?
Give a reason for your answer.
Answer
\({x^2} = {30^2} + {14^2}\)
\({x^2} = 900 + 196\)
\({x^2} = 1096\)
\(x = \sqrt {1096}\)
\(= 33.1\,(to\,1\,decimal\,place)\)
Yes, regulations are being met because 33.1m is less than 35m.
Question
A support beam under a roof space must be at least 2 metres high.
Would a beam positioned as shown in the diagram be acceptable?
Give a reason for your answer.
\({4^2} = {x^2} + {3.5^2}\)
\({x^2} = {4^2} - {3.5^2}\)
\({x^2} = 16 - 12.25\)
\({x^2} = 3.75\)
\(x = \sqrt {3.75}\)
\(= 1.936\,(to\,3\,decimal\,places)\)
No, this position would not be acceptable because 1.936 is less than 2.
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