Question

In $\Delta RST,\angle S={90}^o,\angle T={45}^o,RT=12cm$. Find $RS$ and $ST$.

Answer 1

In $△RST$

$\angle S={90}^{\circ }$

$\angle T={45}^{\circ }$

$RT=12cm$

$\angle R={180}^{\circ }-\angle S-\angle T$ $[\because$ Sum of all 3 sides of a triangle in supplementary]

$={180}^{\circ }-{90}^{\circ }-{45}^{\circ }$

$\angle R={45}^{\circ }$

$\sin T=\frac{RS}{RT}$

$\Rightarrow \sin {45}^{\circ }=\frac{RS}{12}$

$\Rightarrow \frac{1}{\sqrt{2}}=\frac{RS}{12}$

$\Rightarrow RS=6\sqrt{2}$

$\because \angle R=\angle T$

$\Rightarrow ST=RS$ [Sides opposite in equal angle are equal]

$\Rightarrow ST=6\sqrt{2}$ [From above 2 equations]

Hence $RS=6\sqrt{2}$

$ST=6\sqrt{2}$