Question

let right triangle acb have c = 90°, and let sides a, b, and c be opposite angles a, b, and c, respectively. if a = 5 and b = 12, find c. answer exactly. c =

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\) where \(c\) is the hypotenuse and \(a,b\) are the legs of the right - triangle.

Step2: Substitute given values

Given \(a = 5\) and \(b = 12\), we have \(c^{2}=5^{2}+12^{2}\). Then \(c^{2}=25 + 144=169\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c\) represents the length of a side of a triangle (\(c>0\)), \(c=\sqrt{169}=13\).

Answer:

13