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

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Solution

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

By 30^∘− 60^∘ − 90^∘ theorem,

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

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

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

In ∆RST, ∠S = 90∘, ∠T = 30∘, ∴ ∠R = 60∘ By 30∘ − 60∘ − 90∘ theorem, RS=12×RT⇒RS=12×12⇒RS=6 cm ...1ST=32×RT⇒ST=32×12⇒ST=63 cm ...2 Hence, RS = 6 cm and ST = 63 cm.