Question

find the angle α that satisfies the following equation, where ( 0^circ leq alpha leq 90^circ ). do not use a calculator. (cos(alpha)=\frac{sqrt{3}}{2}) (alpha=square^circ) (type an integer or a decimal.)

Explanation:

Step1: Recall cosine values of special angles

We know the cosine values of special angles in the first quadrant (\(0^{\circ}\leq\alpha\leq90^{\circ}\)). For a \(30^{\circ}\) angle, \(\cos(30^{\circ})=\frac{\sqrt{3}}{2}\).

Step2: Identify the angle

Given \(\cos(\alpha)=\frac{\sqrt{3}}{2}\) and \(0^{\circ}\leq\alpha\leq90^{\circ}\), by the definition of cosine for special angles, we can conclude that \(\alpha = 30^{\circ}\) since the cosine of \(30^{\circ}\) is \(\frac{\sqrt{3}}{2}\).

Answer:

\(30\)