#### Question

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

#### Solution

In ∆RST,

∠S = 90^{∘}, ∠T = 30^{∘}, ∴ ∠R = 60^{∘}

By 30^{∘ }− 60^{∘} − 90^{∘} theorem,

\[RS = \frac{1}{2} \times RT\]

\[ \Rightarrow RS = \frac{1}{2} \times 12\]

\[ \Rightarrow RS = 6 cm . . . \left( 1 \right)\]

\[ST = \frac{\sqrt{3}}{2} \times RT\]

\[ \Rightarrow ST = \frac{\sqrt{3}}{2} \times 12\]

\[ \Rightarrow ST = 6\sqrt{3} cm . . . \left( 2 \right)\]

\[ \Rightarrow RS = \frac{1}{2} \times 12\]

\[ \Rightarrow RS = 6 cm . . . \left( 1 \right)\]

\[ST = \frac{\sqrt{3}}{2} \times RT\]

\[ \Rightarrow ST = \frac{\sqrt{3}}{2} \times 12\]

\[ \Rightarrow ST = 6\sqrt{3} cm . . . \left( 2 \right)\]

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

Is there an error in this question or solution?

Solution In ∆Rst, ∠S = 90°, ∠T = 30°, Rt = 12 Cm Then Find Rs and St. Concept: Apollonius Theorem.