The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the side labeled x is 16.62 units.
What are Trigonometric functions?
The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]
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 the 90° angle.
In ΔABD, using the trigonometric functions the trigonometric ratios can be written as,
sin(θ) = Perpendicular/Hypotenuse
sin(∠BAD) = BD/AB
sin(43°) = BD/39
sin(43°) × 39 = BD
BD = 26.598 units
Now, in ΔBDC, the trigonometric function can be written as,
tan(θ) = Perpendicular/Base
tan(∠CBD) = CD/BD
tan(32°) = x / 26.598 units
x = 26.598 units × tan(32°)
x = 16.62 units
Hence, the length of the side labelled x is 16.62 units.
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