Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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In ∆Rst, ∠S = 90°, ∠T = 30°, Rt = 12 Cm Then Find Rs and St. - Geometry

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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,

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

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

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 2: Pythagoras Theorem
Problem Set 2 | Q: 3 | Page no. 44
Solution In ∆Rst, ∠S = 90°, ∠T = 30°, Rt = 12 Cm Then Find Rs and St. Concept: Apollonius Theorem.
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