Question

find the value of z in the triangle shown below. choose 1 answer: a (z = sqrt{52}) b (z=sqrt{10}) c (z = sqrt{24}) d (z = 52)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Here \(a = 4\), \(b = 6\), and \(c=z\). So \(4^{2}+6^{2}=z^{2}\).

Step2: Calculate the squares

\(4^{2}=16\) and \(6^{2}=36\). Then \(z^{2}=16 + 36\).

Step3: Find the sum

\(z^{2}=52\).

Step4: Solve for \(z\)

Taking the square root of both sides, \(z=\sqrt{52}\) (we consider the positive square root since \(z\) represents the length of a side of a triangle).

Answer:

A. \(z=\sqrt{52}\)