Question

the pythagorean theorem

1. find the measure of the unknown side.

a)
diagram of right triangle with right angle at c, ac = 8 cm, cb = 6 cm, hypotenuse ab labeled ( c )

Explanation:

Step1: Identify the triangle type

It's a right - triangle with legs \(a = 8\space cm\), \(b = 6\space cm\) and hypotenuse \(c\). Use the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\).

Step2: Substitute values

Substitute \(a = 8\) and \(b = 6\) into the formula: \(c^{2}=8^{2}+6^{2}=64 + 36=100\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{100} = 10\space cm\).

Answer:

The length of the unknown side \(c\) is \(10\space cm\).