Question

find the value of x.
13
10
x = ?
round to the nearest tenth.

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, \(a = 13\), \(b = 10\), and \(c=x\).

Step2: Apply the Pythagorean theorem

Substitute the values of \(a\) and \(b\) into the formula: \(x^{2}=13^{2}+10^{2}\). Calculate \(13^{2}=169\) and \(10^{2} = 100\). Then \(x^{2}=169 + 100=269\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{269}\). Calculate \(\sqrt{269}\approx16.4\) (rounded to the nearest tenth).

Answer:

\(16.4\)