Question

or as a decimal rounded to the hundredths place.
draw
show your work here
hint: to add the square root symbol (√), type
oot\
z =

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 12\), \(b = 13\), and \(c=z\). So \(z^{2}=12^{2}+13^{2}\).

Step2: Calculate squares

\(12^{2}=144\) and \(13^{2}=169\). Then \(z^{2}=144 + 169\).

Step3: Sum the values

\(144+169 = 313\). So \(z=\sqrt{313}\).

Step4: Calculate the decimal value

\(\sqrt{313}\approx17.69\)

Answer:

\(z\approx17.69\)