Tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The value of x is 5.5 yd.
What is Tangent (Tanθ)?
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the value of the ∠ACD is 20°. And we can see that ∠ACD and ∠CAB are alternate interior angles. Therefore, the measure of both the angels will be equal.
∠ACD = ∠CAB = 20°
Now, using the Tangent function of trigonometry, the value of x can be written as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
[tex]\rm Tangent(\angle CAB) = \dfrac{BC}{AB}\\\\\rm Tan(20^o) = \dfrac{x}{15}\\\\x = tan(20^o) \times 15\\\\x = 5.4596\approx 5.5 yd[/tex]
Hence, the value of x is 5.5 yd.
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