Triangle PRQ is half of an equilateral triangle. If angle P  is 30°  is What is the value of cos 30° ?

1. Break Down the Problem

We need to find the value of $\cos 30^\circ$. In an equilateral triangle, all angles are $60^\circ$, but since angle $P$ of triangle $PRQ$ is given as $30^\circ$, we can directly compute the cosine of $30^\circ$.

2. Relevant Concepts

We know that the cosine function can be defined in terms of the sides of a right triangle or using the unit circle. Specifically, we can use the well-known trigonometric value for $\cos 30^\circ$.

3. Analysis and Detail

The value of $\cos 30^\circ$ is derived from the properties of 30-60-90 triangles, where:

• The ratio of the sides opposite to the $30^\circ$, $60^\circ$, and $90^\circ$ angles are $1:\sqrt{3}:2$.

Thus, for an angle of $30^\circ$:

$\cos 30^\circ = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{\sqrt{3}}{2}$

4. Verify and Summarize

The properties of 30-60-90 triangles are well-established, and the value $\frac{\sqrt{3}}{2}$ is widely recognized as the cosine of $30^\circ$.

Final Answer

$\cos 30^\circ = \frac{\sqrt{3}}{2}$