Question

the diagonal of rectangle abcd measures 2 inches in length. what is the length of line segment ab? 1 inch √3 inches 4 inches 4√3 inches

Explanation:

Step1: Use cosine function

In right - triangle \(ABD\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\) and the hypotenuse \(BD = 2\) inches. The adjacent side to the \(30^{\circ}\) angle is \(AB\).
The formula for \(\cos\theta\) is \(\cos30^{\circ}=\frac{AB}{BD}\).

Step2: Substitute values

Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\) and \(BD = 2\) inches. Substituting into \(\cos30^{\circ}=\frac{AB}{BD}\), we get \(\frac{\sqrt{3}}{2}=\frac{AB}{2}\).

Step3: Solve for \(AB\)

Cross - multiply: \(AB = 2\times\frac{\sqrt{3}}{2}\).

Answer:

\(\sqrt{3}\) inches