Question

find the value of x.
x = ?

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 56\), \(b = 33\) and \(c=x\).

Step2: Apply the Pythagorean theorem

Substitute the values of \(a\) and \(b\) into the formula: \(x^{2}=56^{2}+33^{2}\).
First, calculate \(56^{2}=56\times56 = 3136\) and \(33^{2}=33\times33=1089\).
Then, \(x^{2}=3136 + 1089=4225\).

Step3: Solve for x

Take the square root of both sides: \(x=\sqrt{4225}\). Since \(\sqrt{4225} = 65\) (because \(65\times65 = 4225\)).

Answer:

\(65\)