Question

use the pythagorean theorem to find the length of the hypotenuse of the triangle below. round to two decimal places, if necessary.
show your work here
hint: to add the square root symbol (√), type
oot\
enter your answer

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 13\), \(b = 16\), and \(c\) is the hypotenuse.
Substitute the values: \(13^{2}+16^{2}=c^{2}\).
Calculate \(13^{2}=169\) and \(16^{2}=256\).
Then \(169 + 256=c^{2}\), so \(c^{2}=425\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{425}\).
Simplify \(\sqrt{425}=\sqrt{25\times17}=5\sqrt{17}\approx 20.62\).

Answer:

\(20.62\)