What is the value of 50tan(30) ?

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

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50tan(30)

50 tan (3 0^{\circ})

\frac{50 3}{3}

Decimal

28.86751 \dots

Solution steps

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}

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

Simplify

50 \cdot \frac{3}{3} : \frac{50 3}{3}

50 \cdot \frac{3}{3}

Multiply fractions:

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

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

Apply radical rule:

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

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{50}{3 ^{1 - \frac{1}{2}}}

Subtract the numbers:

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

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

Apply radical rule:

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

= \frac{50}{3}

Rationalize

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

\frac{50}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{50 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{50 3}{3}

= \frac{50 3}{3}

= \frac{50 3}{3}