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In a triangle, the angles are in the ratio 2 : 5 : 3. What is the value of the least angle in the radian? (SSC CGL 1st Sit. 2013)
- a)π/20
- b)π/10
- c)2π/5
- d)π/5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a triangle, the angles are in the ratio 2 : 5 : 3. What is the valu...
Let angles are 2x, 5x and 3x.
2x + 5x + 3x = 180º (sum of interior angle of triangles is 180º)
10x = 18º
x = 18º
∴ Least angle in degree = 2x = 2 × 18 = 36º
2x + 5x + 3x = 180º (sum of interior angle of triangles is 180º)
10x = 18º
x = 18º
∴ Least angle in degree = 2x = 2 × 18 = 36º
Most Upvoted Answer
In a triangle, the angles are in the ratio 2 : 5 : 3. What is the valu...
Understanding the Angle Ratio
In a triangle, the sum of the interior angles is always 180 degrees. Here, the angles are in the ratio of 2:5:3.
Calculating the Angles
- Let the angles be represented as:
- 2x (for the first angle)
- 5x (for the second angle)
- 3x (for the third angle)
- The equation for the sum of angles in a triangle can be set up as follows:
2x + 5x + 3x = 180 degrees
- Simplifying this gives:
10x = 180 degrees
- Solving for x:
x = 18 degrees
Finding Each Angle
- Now substituting x back into the angle expressions:
- First angle = 2x = 2(18) = 36 degrees
- Second angle = 5x = 5(18) = 90 degrees
- Third angle = 3x = 3(18) = 54 degrees
Identifying the Least Angle
- The least angle among these is 36 degrees.
Converting Degrees to Radians
- To convert degrees to radians, use the conversion factor π radians = 180 degrees.
- Therefore, to convert 36 degrees to radians:
Radian Measure = (36 degrees) * (π/180) = π/5 radians
Conclusion
- Thus, the least angle in the triangle, expressed in radians, is:
π/5
The correct answer is option 'D'.
In a triangle, the sum of the interior angles is always 180 degrees. Here, the angles are in the ratio of 2:5:3.
Calculating the Angles
- Let the angles be represented as:
- 2x (for the first angle)
- 5x (for the second angle)
- 3x (for the third angle)
- The equation for the sum of angles in a triangle can be set up as follows:
2x + 5x + 3x = 180 degrees
- Simplifying this gives:
10x = 180 degrees
- Solving for x:
x = 18 degrees
Finding Each Angle
- Now substituting x back into the angle expressions:
- First angle = 2x = 2(18) = 36 degrees
- Second angle = 5x = 5(18) = 90 degrees
- Third angle = 3x = 3(18) = 54 degrees
Identifying the Least Angle
- The least angle among these is 36 degrees.
Converting Degrees to Radians
- To convert degrees to radians, use the conversion factor π radians = 180 degrees.
- Therefore, to convert 36 degrees to radians:
Radian Measure = (36 degrees) * (π/180) = π/5 radians
Conclusion
- Thus, the least angle in the triangle, expressed in radians, is:
π/5
The correct answer is option 'D'.
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