Answer: The correct option is (C) 14.5 cm.
Step-by-step explanation: We are given to find the length of the side BC in the triangle ABC shown in the figure.
From the figure, we see that
triangle ABC is a right-angled triangle, where
[tex]m\angle C=90^\circ,~~m\angle M=65^\circ,~~AB=16~\textup{cm},~~BC=x=?.[/tex]
With respect to angle A, side BC is the perpendicular and AB is the hypotenuse.
So, from trigonometric ratios, we have
[tex]\sin m\angle A=\dfrac{BC}{AB}\\\\\\\Rightarrow \sin65^\circ=\dfrac{x}{16}\\\\\\\Rightarrow 0.9063=\dfrac{x}{16}\\\\\\\Rightarrow x=16\times 0.9063\\\\\Rightarrow x=14.5008.[/tex]
Rounding to the nearest tenth, we get
x = 14.5 cm.
Thus, the length of the side BC is 14.5 cm.
Option (C) is CORRECT.
