The length of the side CD and AB is √3
What are Trigonometric functions?
\(Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)
\(Cos \theta=\dfrac{Base}{Hypotenuse}\)
\(Tan \theta=\dfrac{Perpendicular}{Base}\)
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
Given to us
- BD = 2 inches
- ∠CBD = 60°
- ∠CDB = 30°
In ΔBCD,
For ∠B
\(Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)
\(Sin(\angle B)=\dfrac{CD}{BD}\\\\Sin(60^o)=\dfrac{CD}{2}\\\\CD = 2 \times Sin(60^o)\\\\ CD = 2 \times \dfrac{\sqrt3}{2}\\\\CD = \sqrt3\)
Thus, the length of the side CD is √3.
Length of Side AB
As it is already given that the figure ABCD is a rectangle the length of side AB is equal to CD.
AB = CD = √3
Hence, the length of the side CD and AB is √3.
Learn more about Trigonometric functions:
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