Answer: The required length of AC is 16.1 units.
Step-by-step explanation: We are given to find the length of side AC of triangle ABC.
From the figure, we note that
the triangle ABC is a right-angled triangle, where
m∠C = 90°, m∠A = 32° and BC = 10 units.
For the acute angle A, side AC is the base and side BC is the perpendicular.
So, from trigonometric ratios, we have
[tex]\tan m\angle A=\dfrac{perpendicular}{base}\\\\\\\Rightarrow \tan32^\circ=\dfrac{BC}{AC}\\\\\\\Rightarrow \tan32^\circ=\dfrac{10}{AC}\\\\\\\Rightarrow 0.62=\dfrac{10}{AC}\\\\\\\Rightarrow AC=\dfrac{10}{0.62}\\\\\Rightarrow AC=16.13.[/tex]
Rounding to nearest tenth, we get
AC = 16.1 units.
Thus, the required length of AC is 16.1 units.
