Question

find the missing dimension of a right triangle with sides a and b and hypotenuse c. answer exactly.
a = 7, b = 6
c =

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(c^{2}=a^{2}+b^{2}\). Given \(a = 7\) and \(b = 6\), we substitute these values into the formula: \(c^{2}=7^{2}+6^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(7^{2}=49\) and \(6^{2}=36\). So \(c^{2}=49 + 36\).

Step3: Sum the values

\(49+36=85\). Then \(c=\sqrt{85}\) (since \(c>0\) as it represents the length of a side of a triangle).

Answer:

\(\sqrt{85}\)