What is the value of sqrt((183*9.8)/(sin(90))) ?

The value of sqrt((183*9.8)/(sin(90))) is (7sqrt(915))/5

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Popular Trigonometry >

sqrt((183*9.8)/(sin(90)))

Solution

\frac{183 \cdot 9.8}{sin ( 9 0 ^{\circ} )}

Solution

\frac{7 915}{5}

Decimal

42.34855 \dots

Solution steps

\frac{183 \cdot 9.8}{sin ( 9 0 ^{\circ} )}

= \frac{183 \cdot \frac{49}{5}}{sin ( 9 0 ^{\circ} )}

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{183 \cdot \frac{49}{5}}{1}

Simplify

\frac{183 \cdot \frac{49}{5}}{1} : \frac{7 915}{5}

\frac{183 \cdot \frac{49}{5}}{1}

\frac{183 \cdot \frac{49}{5}}{1} = \frac{8967}{5}

\frac{183 \cdot \frac{49}{5}}{1}

Multiply

183 \cdot \frac{49}{5} : \frac{8967}{5}

183 \cdot \frac{49}{5}

Multiply fractions:

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

= \frac{49 \cdot 183}{5}

Multiply the numbers:

49 \cdot 183 = 8967

= \frac{8967}{5}

= \frac{\frac{8967}{5}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{8967}{5}

= \frac{8967}{5}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{8967}{5}

8967 = 7183

8967

Prime factorization of

8967 : 3 \cdot 7^{2} \cdot 61

8967

8967

divides by

38967 = 2989 \cdot 3

= 3 \cdot 2989

2989

divides by

72989 = 427 \cdot 7

= 3 \cdot 7 \cdot 427

427

divides by

7427 = 61 \cdot 7

= 3 \cdot 7 \cdot 7 \cdot 61

3, 7, 61

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 7 \cdot 7 \cdot 61

= 3 \cdot 7^{2} \cdot 61

= 7^{2} \cdot 3 \cdot 61

Apply radical rule:

= 7^{2} 3 \cdot 61

Apply radical rule:

7^{2} = 7

= 7 3 \cdot 61

Refine

= 7183

= \frac{7 183}{5}

Rationalize

\frac{7 183}{5} : \frac{7 915}{5}

\frac{7 183}{5}

Multiply by the conjugate

\frac{5}{5}

= \frac{7 183 5}{5 5}

71835 = 7915

71835

Apply radical rule:

a b = a \cdot b

1835 = 183 \cdot 5

= 7 183 \cdot 5

Multiply the numbers:

183 \cdot 5 = 915

= 7915

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= \frac{7 915}{5}

= \frac{7 915}{5}

= \frac{7 915}{5}

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Frequently Asked Questions (FAQ)

What is the value of sqrt((183*9.8)/(sin(90))) ?
The value of sqrt((183*9.8)/(sin(90))) is (7sqrt(915))/5