What is the value of (212.13)/(sin(60)) ?

The value of (212.13)/(sin(60)) is (7071sqrt(3))/(50)

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(212.13)/(sin(60))

\frac{212.13}{sin ( 6 0 ^{\circ} )}

\frac{7071 3}{50}

Decimal

244.94662 \dots

Solution steps

\frac{212.13}{sin ( 6 0 ^{\circ} )}

= \frac{\frac{21213}{100}}{sin ( 6 0 ^{\circ} )}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{\frac{21213}{100}}{\frac{3}{2}}

Simplify

\frac{\frac{21213}{100}}{\frac{3}{2}} : \frac{7071 3}{50}

\frac{\frac{21213}{100}}{\frac{3}{2}}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{21213 \cdot 2}{100 3}

Multiply the numbers:

21213 \cdot 2 = 42426

= \frac{42426}{100 3}

Cancel the common factor:

2

= \frac{21213}{50 3}

Factor

21213 : 3^{2} \cdot 2357

Factor

21213 = 3^{2} \cdot 2357

= \frac{3 ^{2} \cdot 2357}{50 3}

Cancel

\frac{3 ^{2} \cdot 2357}{50 3} : \frac{2357 \cdot 3 ^{\frac{3}{2}}}{50}

\frac{3 ^{2} \cdot 2357}{50 3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3 ^{2} \cdot 2357}{50 \cdot 3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{2}}{3 ^{\frac{1}{2}}} = 3^{2 - \frac{1}{2}}

= \frac{2357 \cdot 3 ^{- \frac{1}{2} + 2}}{50}

Subtract the numbers:

2 - \frac{1}{2} = \frac{3}{2}

= \frac{2357 \cdot 3 ^{\frac{3}{2}}}{50}

= \frac{2357 \cdot 3 ^{\frac{3}{2}}}{50}

3^{\frac{3}{2}} = 33

3^{\frac{3}{2}}

3^{\frac{3}{2}} = 3^{1 + \frac{1}{2}}

= 3^{1 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 3^{1} \cdot 3^{\frac{1}{2}}

Refine

= 33

= \frac{2357 \cdot 3 3}{50}

Multiply the numbers:

2357 \cdot 3 = 7071

= \frac{7071 3}{50}

= \frac{7071 3}{50}

What is the value of (212.13)/(sin(60)) ?
The value of (212.13)/(sin(60)) is (7071sqrt(3))/(50)