Question

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

Explanation:

Step1: Identify right triangle

Triangle ABD is right-angled at A. Diagonal BD = 2 inches, $\angle ADB = 30^\circ$.

Step2: Use cosine for adjacent side

$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, so $\cos(30^\circ) = \frac{AB}{BD}$

Step3: Substitute values and solve

$\cos(30^\circ) = \frac{\sqrt{3}}{2}$, $BD=2$.
$AB = BD \times \cos(30^\circ) = 2 \times \frac{\sqrt{3}}{2}$

Answer:

$\sqrt{3}$ inches