= (30 × 3600)" + (30 × 60)" + 30"

= 108000" + 1800" + 30"

= 109830"

= 18° + (\(\frac{30}{60}\))° + (\(\frac{15}{60×60}\))°

= 18°+ (\(\frac{30}{60}\))°+ (\(\frac{15}{3600}\))°

= (\(\frac{18×3600 + 60×30 + 15}{3600}\))°

= (\(\frac{66615}{3600}\))°

= 18.5042°

= (50 × 10000)" + (49 × 100)" + 38"

= 500000" + 4900" 38"

= 504938"

= 50^{g} + (\(\frac{87}{100}\))^{g} + (\(\frac{50}{100×100}\))^{g}

= 50^{g} + (\(\frac{87}{100}\))^{g} + (\(\frac{50}{10000}\))^{g}

= 50^{g} + 0.87^{g} + 0.005^{g}

= (50+0.87+0.005)^{g}

= 50.875^{g}

Here,

x = 72°

we have,

or, x° = (\(\frac{10}{9}×x\))^{g}

or, 72° = (\(\frac{10}{9}×72\))^{g}

∴ 72° = 80^{g}

Here,

or, x = 60°

we have,

or, x^{g}= (\(\frac{9}{10}×x\))°

or, 60^{g} = (\(\frac{9}{10}×60\))°

∴, 54°

Here,

or, x = 60°

we have,

or, x° = (\(\frac{π}{180}×x\))^{c}

or, 60° = (\(\frac{π}{180}×60\))^{c}

= \(\frac{π^c}{3}\)

Here,

or, x = 75^{g}

we have,

or, x° = (\(\frac{π}{200}×x\))^{c}

∴, 75^{g}=(\(\frac{π}{200}×75\))^{c}

^{}= \(\frac{3π^c}{8}\)

Here,

or, x = \(\frac{2π^c}{5}\)

we have,

or, x^{c} = (\(\frac{180}{π}×x\))°

∴ \(\frac{2π^c}{5}\) = (\(\frac{180}{π}\) × \(\frac{2π}{5}\))°

= 72°

Here,

or, x = \(\frac{4π^c}{5}\)

we have,

or, x^{c} = (\(\frac{200}{π}×x\))^{g}

∴ \(\frac{4π^c}{5}\) = (\(\frac{200}{π}\) ×\(\frac{4π}{5}\))^{g}

= 160^{g}

or, 27° 30' = 27° + (\(\frac{30}{60}\))°

= 27° + (\(\frac{1}{2}\))°

= (\(\frac{55}{2}\))°

∴ 27° 30' = (\(\frac{55}{2}\) × \(\frac{10}{9}\))^{g}

= (\(\frac{275}{9}\))^{g}

Here,

or, 42^{g}60' = 42^{g}+ (\(\frac{60}{100}\))^{g}

= 42^{g}+ (\(\frac{3}{5}\))^{g}

= (42.6)^{g}

= (\(42.6 × \frac{9}{10}\))°

= 38.34°

Here,

\(\angle\)A = 60°, \(\angle\)B = 90°

Now,

\(\angle\)A + \(\angle\)B + \(\angle\)C = 180°

or, 60° + 90° + \(\angle\)C = 180°

or, \(\angle\)C = 180° − 150°

or, \(\angle\)C = 30°

Then,

or, 1° = (\(\frac{10}{9}\))^{g}

or, \(\angle\)A = 60° = (\(60×\frac{10}{9}\))^{g} = (\(\frac{200}{3}\))^{g}

or, \(\angle\)B = 90° = (\(90×\frac{10}{9}\))^{g} = 100^{g}

or, \(\angle\)C = 30° = (\(30×\frac{10}{9}\))^{g} = (\(\frac{100}{3}\))^{g}

solution:

In 60 minutes, the minutes hand makes 360°

In 1 minute, the minute hand makes (\(\frac{360}{60}\))°In 15 minutes, the minute hand makes (\(\frac{360×15}{60}\))° = 90°

Hence, a minute hand makes 90° in 15 minutes.

Solution:

Here,

x = 100

we have,

or, x^{g} = (\(\frac{π}{200} × x \))^{c}

or, 100^{g}= (\(\frac{π}{200} × 100 \))^{c}∴ 100^{g}= (\(\frac{π}{2}\))^{c}