Question

use the pythagorean theorem to find z.
draw
3
4
show your work here
hint: to add the square root symbol ($\sqrt{\square}$), type
o

Explanation:

Step1: Write the Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 3\), \(b = 4\), and \(c=z\). So \(3^{2}+4^{2}=z^{2}\).

Step2: Calculate \(3^{2}\) and \(4^{2}\)

\(3^{2}=9\) and \(4^{2}=16\). Then \(9 + 16=z^{2}\), so \(z^{2}=25\).

Step3: Solve for \(z\)

Take the square root of both sides. Since \(z\) represents the length of a side of a triangle (\(z>0\)), \(z=\sqrt{25}=5\).

Answer:

5