What is the value of (24)/(tan(60)) ?

The value of (24)/(tan(60)) is 8sqrt(3)

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(24)/(tan(60))

\frac{24}{tan ( 6 0 ^{\circ} )}

83

Decimal Notation

13.85640 \dots

Solution steps

\frac{24}{tan ( 6 0 ^{\circ} )}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 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}

= 3

= \frac{24}{3}

Simplify

\frac{24}{3} : 83

\frac{24}{3}

Factor

24 : 2^{3} \cdot 3

Factor

24 = 2^{3} \cdot 3

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

Cancel

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

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

Apply radical rule:

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= 2^{3} 3

= 2^{3} 3

2^{3} = 8

= 83

= 83

\frac{20}{tan ( 3 8 ^{\circ} )}

arccos (\frac{6}{43})

98 cos (3 0^{\circ})

cot (\frac{7 π}{9})

20 tan (6)