The trigonometric function gives the ratio of different sides of a right-angle triangle.The correct option is C.
What is 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 to the 90° angle.
Let the length of the line segement CD be represented by x.
In ΔABC, Using the pythgorus theorem, we can write,
AB² = BC² + AC²
AB² = 30² + 16²
AB = 34 units
In ΔABC, the measure of ∠A be written as,
tan(∠A) = BC/AC
tan(∠A) = 30/16
∠A = tan⁻¹ (30/16)
∠A = 61.9275°
Now, in ΔABD, the measure of ∠A can be written as,
Cos(∠A) = AB/AD
Cos(61.9275°) = 34/(AC+CD)
0.47 = 34/(16+CD)
16 + CD = 72.25
CD = 56.25 ≈ 56
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