What is the value of (20)/(tan(30)) ?

The value of (20)/(tan(30)) is 20sqrt(3)

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(20)/(tan(30))

\frac{20}{tan ( 3 0 ^{\circ} )}

203

Decimal Notation

34.64101 \dots

Solution steps

\frac{20}{tan ( 3 0 ^{\circ} )}

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{20}{\frac{3}{3}}

Simplify

\frac{20}{\frac{3}{3}} : 203

\frac{20}{\frac{3}{3}}

Apply the fraction rule:

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

= \frac{20 \cdot 3}{3}

Multiply the numbers:

20 \cdot 3 = 60

= \frac{60}{3}

Factor

60 : 2^{2} \cdot 3 \cdot 5

Factor

60 = 2^{2} \cdot 3 \cdot 5

= \frac{2 ^{2} \cdot 3 \cdot 5}{3}

Cancel

\frac{2 ^{2} \cdot 3 \cdot 5}{3} : 2^{2} 3 \cdot 5

\frac{2 ^{2} \cdot 3 \cdot 5}{3}

Apply radical rule:

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

= \frac{2 ^{2} \cdot 3 \cdot 5}{3 ^{\frac{1}{2}}}

Apply exponent rule:

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

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

= 2^{2} \cdot 5 \cdot 3^{- \frac{1}{2} + 1}

Subtract the numbers:

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

= 2^{2} \cdot 5 \cdot 3^{\frac{1}{2}}

Apply radical rule:

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

= 2^{2} \cdot 53

= 2^{2} 3 \cdot 5

2^{2} = 4

= 4 \cdot 53

Multiply the numbers:

4 \cdot 5 = 20

= 203

= 203

arctan (- 0.27)

sinh (\frac{7}{20})

sin (4 5^{\circ}) + tan (3 0^{\circ})

csc (4 7^{\circ})

arctan (\frac{3}{12})