Question

ABCD is a quadrilateral.

Work out the length of CD.

Give your answer correct to

3 significant figures.

Answer 1

When measuring the length of side CD of a quadrilateral to three significant figures, one must carefully observe the ruler, use the tick marks for the closest precision, and then estimate the final value for the third significant digit.

Step-by-step explanation:

The question provided requires determining the length of side CD of a quadrilateral ABCD using measurements. Measurements reported to three significant figures are crucial for accuracy and precision. An example can demonstrate how to measure to the correct number of significant figures. Suppose the measurement for CD falls between two marked values on a ruler. If the measurement is between 6.0 cm and 7.0 cm, it is at least 6.0 cm. If it is between the sixth and seventh tick marks past 6.0 cm (assuming each tick represents 0.1 cm), then it is at least 6.6 cm. Estimating further, if it appears to be a bit more than halfway past the sixth tick mark, you might assess the length as 6.65 cm. This final measurement would be reported as the length of CD, accurate to three significant figures.

Answer 2

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