Question

based on the given angle measures, which triangle has side length measures that could be correct?

Explanation:

Step1: Recall the properties of a 30 - 60 - 90 triangle

In a right - angled triangle with angles \(30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\), the side lengths are in the ratio \(1:\sqrt{3}:2\). Let the side opposite the \(30^{\circ}\) angle be \(x\), the side opposite the \(60^{\circ}\) angle be \(x\sqrt{3}\), and the hypotenuse be \(2x\).

Step2: Check each triangle

• First triangle:

If the side opposite \(30^{\circ}\) is \(9\), then the hypotenuse should be \(2\times9 = 18\), but the hypotenuse is \(13.9\). So, this is incorrect.

• Second triangle:

If the side opposite \(30^{\circ}\) is \(8\), then the hypotenuse should be \(2\times8=16\). The side opposite \(60^{\circ}\) should be \(8\sqrt{3}\approx8\times1.732 = 13.856\approx13.9\). This satisfies the side - length ratios of a \(30 - 60 - 90\) triangle.

• Third triangle:

If the side opposite \(30^{\circ}\) is \(13.9\), then the hypotenuse should be \(2\times13.9 = 27.8
eq16\). So, this is incorrect.

• Fourth triangle:

If the side opposite \(30^{\circ}\) is \(16\), then the hypotenuse should be \(2\times16 = 32
eq13.9\). So, this is incorrect.

Answer:

The second triangle has side - length measures that could be correct.