Question:
The sides of a triangle are in the ratio
\[
1:\sqrt3:2.
\]
Then the angles opposite to these sides are in the ratio
The sides of a triangle are in the ratio
\[
1:\sqrt3:2.
\]
Then the angles opposite to these sides are in the ratio
Show Hint
The ratio $1:\sqrt3:2$ immediately indicates a $30^\circ$-$60^\circ$-$90^\circ$ triangle.
Updated On: Jun 3, 2026
- $1:2:3$
- $1:3:2$
- $2:3:1$
- $1:2:2$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Compare the side ratios with the standard side ratios of a $30^\circ$-$60^\circ$-$90^\circ$ triangle.
Step 2: Meaning
The given ratio is \[ 1:\sqrt3:2. \] This is exactly the side ratio of a right triangle with angles \[ 30^\circ,\;60^\circ,\;90^\circ. \]
Step 3: Analysis
The side opposite $30^\circ$ is proportional to $1$. The side opposite $60^\circ$ is proportional to $\sqrt3$. The side opposite $90^\circ$ is proportional to $2$. Hence the angles are \[ 30^\circ:60^\circ:90^\circ. \] Dividing by $30^\circ$, \[ 1:2:3. \]
Step 4: Conclusion
Therefore the required ratio is \[ 1:2:3. \]
Final Answer: (A)
Compare the side ratios with the standard side ratios of a $30^\circ$-$60^\circ$-$90^\circ$ triangle.
Step 2: Meaning
The given ratio is \[ 1:\sqrt3:2. \] This is exactly the side ratio of a right triangle with angles \[ 30^\circ,\;60^\circ,\;90^\circ. \]
Step 3: Analysis
The side opposite $30^\circ$ is proportional to $1$. The side opposite $60^\circ$ is proportional to $\sqrt3$. The side opposite $90^\circ$ is proportional to $2$. Hence the angles are \[ 30^\circ:60^\circ:90^\circ. \] Dividing by $30^\circ$, \[ 1:2:3. \]
Step 4: Conclusion
Therefore the required ratio is \[ 1:2:3. \]
Final Answer: (A)
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