Question

ABCD is a quadrilateral work out CD

Answer 1

In a quadrilateral ABCD, the measure of the length of the quadrilateral CD will be 25.98 cm.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The length of AD will be

tan θ = AB/AD

AD = 12/ tan 35

AD = 17.14 cm

Then the value of the BD will be given by the Pythagoras.

BD² = AB² + AD²

BD² = 12² + 17.14²

BD² = 144 + 239.78

BD² = 437.78

BD = 20.92 cm

Then operate the sine rule in triangle BCD, we have

$\dfrac{BD}{\sin C} = \dfrac{CD }{\sin B}\\\\\\\dfrac{20.92}{\sin 52} = \dfrac{CD }{\sin 102}\\\\\\CD = \dfrac{20.92 \times \sin 102}{\sin 52}$

On further solving, the value of CD will be

CD = 25.98

More about the trigonometry link is given below.

brainly.com/question/22698523

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