Question

find the length of side ( x ) to the nearest tenth.

Explanation:

Step1: Use the property of 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\). Let the side opposite to \(30^{\circ}\) be \(a\), the side opposite to \(60^{\circ}\) be \(a\sqrt{3}\), and the hypotenuse be \(2a\). Here, the side opposite to \(30^{\circ}\) is \(\sqrt{10}\).

Step2: Find the hypotenuse \(x\)

Since the hypotenuse \(x = 2a\) and \(a=\sqrt{10}\), then \(x = 2\sqrt{10}\approx2\times3.162 = 6.324\approx6.3\)

Answer:

\(6.3\)