What is the value of (50)/(tan(30)) ?

The value of (50)/(tan(30)) is 50sqrt(3)

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(50)/(tan(30))

\frac{50}{tan ( 3 0 ^{\circ} )}

503

Decimal Notation

86.60254 \dots

Solution steps

\frac{50}{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{50}{\frac{3}{3}}

Simplify

\frac{50}{\frac{3}{3}} : 503

\frac{50}{\frac{3}{3}}

Apply the fraction rule:

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

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

Multiply the numbers:

50 \cdot 3 = 150

= \frac{150}{3}

Factor

150 : 5^{2} \cdot 2 \cdot 3

Factor

150 = 5^{2} \cdot 2 \cdot 3

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

Cancel

\frac{2 \cdot 3 \cdot 5 ^{2}}{3} : 23 \cdot 5^{2}

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

Apply radical rule:

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

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= 5^{2} \cdot 23

= 23 \cdot 5^{2}

5^{2} = 25

= 2 \cdot 253

Multiply the numbers:

2 \cdot 25 = 50

= 503

= 503

24 sin (3 0^{\circ})

sec (12 9^{\circ})

arctan (\frac{6.9}{9.8} + 0.2)

\frac{cos ( \frac{π}{4} ) - 1}{sin ( \frac{π}{4} )}

\frac{sec ( π )}{2}