Convert the Systems of Measuring Angles

To convert the systems of measuring angles from one system to the other system.

1. Convert 63°14’51” into circular measure.

Solution:

63°14'51"

= 25299/(400 × 90) Right angle

= 2811/4000 Right angle

= (2811/4000) × (π/2) Radian, [As,1 right angle = π/2 Radian]

= (2811π/8000)^c

2. Convert 100^g45’24” in right angles.

Solution:

100^g45'24"

= 100g + 45²⁴/₁₀₀)"

= 100^g + (4524/100)'

= 100^g + {⁴⁵²⁴/_{(100 × 100})}^g

= 100^g + (⁴⁵²⁴/₁₀₀₀₀)^g

= (100¹¹³¹/₂₅₀₀)^g

= (²⁵¹¹³¹/₂₅₀₀)^g

= (²⁵¹¹³¹/_{2500 × 100}) Right angles

= (²⁵¹¹³¹/₂₅₀₀₀₀) Right angles

= 1¹¹³¹/₂₅₀₀₀₀ Right angles

3. Convert 63°14'51" into centesimal measure.

Solution:

63°14'51"

= 63° + (14⁵¹/₆₀) [Since, 1' = 60"]

= 63°+ (297/20)'

= {63²⁹⁷/_{(20 × 60)}}° [Since, 60' = 1°]

= (25299/400)°

= {²⁵²⁹⁹/_{(400 × 90)}} Right angle [Since, 90° = 1 Right angle]

= [{²⁵²⁹⁹/_{(400 × 90)}} × 100]^g, [Since, 100^g = 1 Right angle]

= 70^g + {(¹¹/₄₀) × 100}, [Since, 1^g = 100']

= 70^g + (27¹/₂)‵

= 70^g 27‵50‶, [Since, 1‵ = 100‶]

4. Convert 145°10'48" in right angles

Solution:

145°10'48"

= 145° + (10⁴⁸/₆₀)' [Since, 60" = 1']

= 145° + (54/5)'

= 145° + {54/(5 × 60)}° [Since, 60' = 1°]

= 145° + (9/50)°

= (7259/50)°

= 7259/(50 × 90) Right angles

= 1²⁷⁵⁹/₄₅₀₀ Right angles

● Measurement of Angles