The length of CD to 3 significant figures is 26.1 cm.
What is the length of CD?
The sum of interior angles of a quadrilateral is 360°, each angle of a regular quadrilateral is 90°
BDC is a triangle and angles in a triangle sum up to 180°.
∠BDC = 180 - 102° + 52°
= 180 - 154
∠BDC = 26°
Angle ABD (sum of interior angles in a triangle is 180°)
∠ABD = 180 - 90 - 35
∠ABD = 55°
Side BD:
sin 35° = opposite/hypotenuse
sin 35° = 12/BD
BD sin 35° = 12
BD = 12/sin 35°
BD = 12/0.57357643635
BD = 20.9213615475
BD ≈ 21 cm
Using sine formula we can find CD
21/sin 52° = DC/sin 102°
CD sin 52° = 21 sin 102°
CD = 21 sin 102°/sin 52°
CD = 0.97814760073 × 21/0.7880107536
CD = 20.5410996154 /0.7880107536
CD = 26.0670295696
CD ≈ 26.1 cm
Hence, CD equals 26.1 cm