What is the value of (9.8sin(120))/(sin(90)) ?

The value of (9.8sin(120))/(sin(90)) is (49sqrt(3))/(10)

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(9.8sin(120))/(sin(90))

\frac{9.8 sin ( 12 0 ^{\circ} )}{sin ( 9 0 ^{\circ} )}

\frac{49 3}{10}

Decimal

8.48704 \dots

Solution steps

\frac{9.8 sin ( 12 0 ^{\circ} )}{sin ( 9 0 ^{\circ} )}

= \frac{\frac{49}{5} sin ( 12 0 ^{\circ} )}{sin ( 9 0 ^{\circ} )}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

sin (x)

periodicity table with

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

periodicity table with

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= \frac{\frac{49}{5} \cdot \frac{3}{2}}{1}

Simplify

\frac{\frac{49}{5} \cdot \frac{3}{2}}{1} : \frac{49 3}{10}

\frac{\frac{49}{5} \cdot \frac{3}{2}}{1}

Multiply

\frac{49}{5} \cdot \frac{3}{2} : \frac{49 3}{10}

\frac{49}{5} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{49 3}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{49 3}{10}

= \frac{\frac{49 3}{10}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{49 3}{10}

= \frac{49 3}{10}

What is the value of (9.8sin(120))/(sin(90)) ?
The value of (9.8sin(120))/(sin(90)) is (49sqrt(3))/(10)