Question

find the length of \\( \overline { a c } \\)

Explanation:

Step1: Recall the cosine formula

In a right - triangle \(ABC\) (\(\angle B = 90^{\circ}\)), \(\cos C=\frac{BC}{AC}\).

Step2: Substitute the known values

Given \(\angle C = 60^{\circ}\) and \(BC = 5\). We know that \(\cos60^{\circ}=\frac{1}{2}\). From \(\cos C=\frac{BC}{AC}\), we can rewrite it as \(AC=\frac{BC}{\cos C}\).
Substitute \(BC = 5\) and \(\cos C=\cos60^{\circ}=\frac{1}{2}\) into the formula: \(AC=\frac{5}{\cos60^{\circ}}\).

Step3: Calculate the value of \(AC\)

Since \(\cos60^{\circ}=\frac{1}{2}\), then \(AC=\frac{5}{\frac{1}{2}}=10\).

Answer:

10