Question

In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm then find RS and ST.

Answer 1

In ∆RST,
∠S = 90^∘, ∠T = 30^∘, ∴ ∠R = 60^∘
By 30^∘ − 60^∘ − 90^∘ theorem,

\[RS = \frac{1}{2} \times RT\]
\[ \Rightarrow RS = \frac{1}{2} \times 12\]
\[ \Rightarrow RS = 6 cm . . . \left( 1 \right)\]
\[ST = \frac{\sqrt{3}}{2} \times RT\]
\[ \Rightarrow ST = \frac{\sqrt{3}}{2} \times 12\]
\[ \Rightarrow ST = 6\sqrt{3} cm . . . \left( 2 \right)\]

Hence, RS = 6 cm and ST = 6\[\sqrt{3}\] cm.