Question

find the unknown side (in cm) of the triangle. round to the nearest tenth. triangle with legs 4 cm and 6 cm, right - angled

Explanation:

Step1: Identify triangle type (right triangle)

This is a right - triangle with legs \(a = 4\space cm\) and \(b=6\space cm\). We use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse (unknown side).

Step2: Substitute values into formula

Substitute \(a = 4\) and \(b = 6\) into the formula: \(c=\sqrt{4^{2}+6^{2}}=\sqrt{16 + 36}=\sqrt{52}\)

Step3: Calculate and round

\(\sqrt{52}\approx7.211\), and when rounded to the nearest tenth, we get \(7.2\)

Answer:

\(7.2\)