Question

directions: find the value of x.
1.
2.

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, \(a = 10\), \(b = 7\) and \(c=x\).

Step2: Apply the Pythagorean theorem

Substitute the values of \(a\) and \(b\) into the formula: \(x^{2}=10^{2}+7^{2}\)
Calculate \(10^{2}=100\) and \(7^{2} = 49\), so \(x^{2}=100 + 49=149\)

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{149}\approx12.21\) (if we want a decimal approximation) or we can leave it as \(\sqrt{149}\)

Answer:

\(x = \sqrt{149}\) (or approximately \(12.21\))