Class 11 RS Aggarwal Chapter-14 Measurement of Angles Solutions - Free PDF Download
FAQs on RS Aggarwal Class 11 Solutions Chapter-14 Measurement of Angles
1. What are the three main systems for measuring angles covered in RS Aggarwal Class 11 Chapter 14?
Chapter 14 of RS Aggarwal Class 11 solutions details three primary systems for measuring angles:
- Sexagesimal System: This is the most common system, where a right angle is divided into 90 degrees (90°). Each degree is further divided into 60 minutes (60'), and each minute into 60 seconds (60").
- Centesimal System: Also known as the French system, it divides a right angle into 100 grades (100g). Each grade is divided into 100 minutes, and each minute into 100 seconds.
- Circular System: This system measures angles in radians. One radian is the angle formed at the centre of a circle by an arc whose length is equal to the radius of the circle.
2. How do you correctly convert an angle from the Sexagesimal (degree) system to the Circular (radian) system for problems in this chapter?
To convert any angle from degrees to radians, you must use the fundamental relationship that π radians = 180°. The correct method is to multiply the angle in degrees by the conversion factor (π/180). For instance, to solve for 60°, the calculation would be 60 × (π/180), which simplifies to π/3 radians. This conversion is a crucial first step for many problems in the exercises.
3. What is the step-by-step method to solve problems involving the relation θ = l/r in RS Aggarwal Chapter 14?
To correctly solve problems using the formula θ = l/r (where 'l' is arc length and 'r' is the radius), follow these essential steps as per the solutions:
- First, identify the given values for the angle (θ), arc length (l), and radius (r).
- The most critical step is to ensure the angle θ is expressed in radians. If the angle is given in degrees, you must convert it first.
- Substitute the known values into the formula.
- Solve for the unknown variable, ensuring that the units for length ('l') and radius ('r') are consistent.
4. How do the types of questions in RS Aggarwal for 'Measurement of Angles' build upon the concepts in the NCERT syllabus?
While NCERT lays the foundation for degrees and radians, RS Aggarwal solutions for Chapter 14 provide a greater variety and complexity of application-based problems. Students will find more extensive practice on:
- Complex problems involving the angle between the hands of a clock at specific times.
- Questions on finding the angles of regular polygons with a larger number of sides.
- Detailed exercises on the relationship between all three measurement systems using the formula D/90 = G/100 = 2R/π.
- Application problems involving circular motion, such as a train on a curved track or a swinging pendulum.
5. What is a common mistake to avoid when calculating the angle between the hands of a clock, a frequent problem type in this chapter?
A common mistake is calculating the angle based only on the fixed positions of the numbers on the clock face. The correct method requires calculating the precise angle traced by both the minute and hour hands independently from the 12 o'clock position. Students often forget to account for the continuous movement of the hour hand as the minute hand moves, which leads to an incorrect answer.
6. Why is it essential to use radians, not degrees, when applying the formula relating arc length and the radius of a circle?
The formula θ = l/r is fundamentally derived from the very definition of a radian. A radian is a 'pure' or dimensionless unit that represents the ratio of arc length to the radius. The simple relationship where the angle is directly proportional to the arc length only holds true when the angle is measured in radians. Using degrees would require incorporating a conversion factor (like π/180) into the formula, making it unnecessarily complex.
7. How are the interior angles of a regular polygon calculated using concepts from this chapter's solutions?
The solutions in RS Aggarwal guide you to calculate the measure of each interior angle of a regular polygon with 'n' sides using a two-step process:
- First, find the sum of all interior angles using the formula: Sum = (n - 2) × 180°.
- Next, since the polygon is regular, all its interior angles are equal. Therefore, divide the total sum by the number of sides 'n' to find the measure of a single angle: Each Interior Angle = [(n - 2) × 180°] / n.
This value in degrees can then be converted to radians if the question requires it.
