SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Right-angled Triangles, SM-Bank 028

Find the value of the pronumeral in the right-angled triangle below correct to one decimal place.  (2 marks)

Show Answers Only

\(x=5.7\ \text{(1 d.p.)}\)

Show Worked Solution

\(\text{Pythagoras’ Theorem states:  }a^2+b^2=c^2\)

\(\text{Let }a=x ,\ b=4\ \text{and }c=7\)

\(x^2+4^2\) \(=7^2\)
\(x^2+16\) \(=49\)
\(x^2\) \(=49-16\)
\(x^2\) \(=33\)
\(\therefore x\) \(=\sqrt{33}\)
  \(=5.744\dots\approx 5.7\ \text{(1 d.p.)}\)