Solving problems using Pythagoras' theorem
Example
A post is \(30\,m\) high.
A cable is attached to the top of the post.
The other end of the cable is \(14\,m\) from the base of the post.
Regulations state that the cable must measure less than \(35\,m\).
Are the regulations being met?
Give a reason for your answer.
\(x^{2} = 30^{2} + 14^{2}\)
\(x^{2} = 900 + 196\)
\(x^{2} = 1096\)
\(x = \sqrt {1096}\)
\(x = 33.1\,(to\,1\,d.p.)\)
Regulations are being met because \(33.1\,m\) is less than \(35\,m\).
The reason you give must be compared to the rule given in the question.
Question
A support beam under a roof space must be at least \(2\,m\) high.
Would a beam positioned as shown in the diagram be acceptable?
Give a reason for your answer.
\(4^{2} = x^{2} + 3.5^{2}\)
\(x^{2} = 4^{2} - 3.5^{2}\)
\(x^{2} = 16 - 12.25\)
\(x^{2} = 3.75\)
\(x = \sqrt {3.75}\)
\(x = 1.936\,(to\,3\,d.p.)\)
No, this position would not be acceptable because 1.936 is less than 2.
