The sides of the parallelogram are 6 and 16, respectively, and its obtuse angle is 120 degrees

The sides of the parallelogram are 6 and 16, respectively, and its obtuse angle is 120 degrees. find the length of the smaller diagonal.

Let us introduce the notation.
ABCD – Conditional parallelogram.
AB = 6, BC = 16, ∠ ABC = 120 °, ∠ BAC = 180 ° – ∠ ABC = 60 ° (one-sided corners).
From vertex B to side AD, we lower the height BH. Consider a right-angled triangle ABH:
∠ ABH = 90 ° – 60 ° = 30 °.
The AН leg lies opposite an angle of 30 ° and is equal to:
AH = 1/2 * AB = 3.
BH = √ (AB² – AH²) = √ (36 – 9) = √27 = 2√3.
Consider a right-angled triangle BHD:
HD = AD – AH = 16 – 3 = 13.
BD = √ (BH² + HD²) = √ (27 + 169) = √196 = 14.
Answer: the length of the smaller diagonal is 14.