Question

In the adjoining figure, ∆ABC is a right-angled at B and ∠A = 45°. If AC = $3\sqrt{2}$ cm,
find (i) BC, (ii) AB.
Figure

Answer 1

From right-angled ∆ABC, we have:
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$$\begin{gathered} \frac{BC}{AC}=\sin {45}^{\mathrm{o}} \\ \Rightarrow \frac{BC}{3\sqrt{2}}=\frac{1}{\sqrt{2}}\Rightarrow BC=3\mathrm{cm} \\ \mathrm{Also},\frac{AB}{AC}=\cos {45}^o \\ \Rightarrow \frac{AB}{3\sqrt{2}}=\frac{1}{\sqrt{2}}\Rightarrow AB=3\mathrm{cm} \\ \therefore BC=3\mathrm{cm}\mathrm{and}AB=3\mathrm{cm} \end{gathered}$$