Question

10/30 pythagorean theorem - basics
find the missing side:
34
30

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the missing side be \(a\), \(b = 30\), and \(c=34\). Then \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute the values

Substitute \(b = 30\) and \(c = 34\) into the formula: \(a^{2}=34^{2}-30^{2}\).
Calculate \(34^{2}=34\times34 = 1156\) and \(30^{2}=30\times30=900\).
So \(a^{2}=1156 - 900=256\).

Step3: Find the value of \(a\)

Take the square root of \(a^{2}\). Since \(a>0\) (length of a side), \(a=\sqrt{256}=16\).

Answer:

\(16\)