Question

find the length of side x to the nearest tenth. triangle with angles 30°, 60°, right angle, hypotenuse √11, side x opposite 30°? wait, no, right angle, so angles 30, 60, 90. hypotenuse? wait, the triangle has a right angle, 30°, 60°, and hypotenuse √11? wait, no, the side labeled √11 is one of the sides, and x is another. wait, the ocr text: find the length of side x to the nearest tenth. triangle image: right-angled, 30° angle, 60° angle, side with √11, side x. answer attempt 2 out of 8

Explanation:

Step1: Identify triangle type and use sine

This is a right - triangle. We know that in a right - triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). For the \(30^{\circ}\) angle, the hypotenuse is \(\sqrt{11}\) and the opposite side to \(30^{\circ}\) is \(x\). So, \(\sin(30^{\circ})=\frac{x}{\sqrt{11}}\).

Step2: Solve for \(x\)

We know that \(\sin(30^{\circ}) = 0.5\). So, we can rewrite the equation as \(x=\sqrt{11}\times\sin(30^{\circ})\). Substitute \(\sin(30^{\circ}) = 0.5\) and \(\sqrt{11}\approx3.3166\) into the equation. Then \(x = 3.3166\times0.5=1.6583\). Rounding to the nearest tenth, we get \(x\approx1.7\).

Answer:

\(1.7\)