What is the value of (2.5)/(tan(30)) ?

The value of (2.5)/(tan(30)) is (5sqrt(3))/2

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(2.5)/(tan(30))

\frac{2.5}{tan ( 3 0 ^{\circ} )}

\frac{5 3}{2}

Decimal Notation

4.33012 \dots

Solution steps

\frac{2.5}{tan ( 3 0 ^{\circ} )}

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

Simplify

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

\frac{\frac{5}{2}}{\frac{3}{3}}

Divide fractions:

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

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

Multiply the numbers:

5 \cdot 3 = 15

= \frac{15}{2 3}

Factor

15 : 3 \cdot 5

Factor

15 = 3 \cdot 5

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

Cancel

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

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

Apply radical rule:

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

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= \frac{5 3}{2}

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

= \frac{5 3}{2}

2 - 2 cos (2 π)

1 sin (4 0^{\circ})

sin^{2} (0.1)

22 sin (3 0^{\circ})

cosh^{2} (2)

What is the value of (2.5)/(tan(30)) ?
The value of (2.5)/(tan(30)) is (5sqrt(3))/2