Answer: The measure of ∠D is 29° approximately.
Step-by-step explanation: We are given a right-angled triangle BCD, where ∠C = 90°, BC = 25 ft and CD = 45 ft.
In ΔBCD, with respect to ∠D, we have
base, b = CD = 45 ft,
perpendicular, p = BC = 25 ft
and
hypotenuse, h = BD.
Therefore, we can write
[tex]\tan \angle D=\dfrac{p}{b}\\\\\Rightarrow \tan \angle D=\dfrac{25}{45}\\\\\Rightarrow \tan \angle D=\dfrac{5}{9}\\\\\Rightarrow \tan \angle D=0.555...\\\\\Rightarrow \angle D=\tan^{-1}(0.555...)\\\\\Rightarrow \angle D\sim 0.506~\textup{radians}.[/tex]
Now,
[tex]\pi~\textup{radians}=180^\circ,\\\\1~\textup{radian}=\dfrac{180^\circ}{\pi},\\\\0.506~\textup{radians}=\dfrac{180^\circ\times 0.506}{\frac{22}{7}}=\dfrac{180^\circ\times 0.506\times 7}{22}=28.98^\circ\sim 29^\circ.[/tex]
Thus, the measure of ∠D is 29° approximately.
