What is the general solution for (sin(53.3))/(20.7)=(sin(x))/(24.9) ?

The general solution for (sin(53.3))/(20.7)=(sin(x))/(24.9) is x=1.30337…+360n,x=180-1.30337…+360n

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(sin(53.3))/(20.7)=(sin(x))/(24.9)

\frac{sin ( 53. 3 ^{\circ} )}{20.7} = \frac{sin ( x )}{24.9}

x = 1.30337 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.30337 \dots + 36 0^{\circ} n

Radians

x = 1.30337 \dots + 2 πn, x = π - 1.30337 \dots + 2 πn

Solution steps

\frac{sin ( 53. 3 ^{\circ} )}{20.7} = \frac{sin ( x )}{24.9}

Switch sides

\frac{sin ( x )}{24.9} = \frac{sin ( 53. 3 ^{\circ} )}{20.7}

Multiply both sides by

24.9

\frac{sin ( x )}{24.9} = \frac{sin ( 53. 3 ^{\circ} )}{20.7}

Multiply both sides by

24.9

\frac{24.9 sin ( x )}{24.9} = \frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}

Simplify

sin (x) = \frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}

sin (x) = \frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}

Apply trig inverse properties

sin (x) = \frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}

General solutions for

sin (x) = \frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}) + 36 0^{\circ} n

x = arcsin (\frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{24.9 sin ( 53. 3 ^{\circ} )}{20.7}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.30337 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.30337 \dots + 36 0^{\circ} n

c, 1 = π (0) - 0 arccos (ln (0) + c)

θ, a (1 + cos (θ)) = 0

cos (θ) = \frac{1}{21}

- \frac{1}{2} = cos (x)

3 sin (x) = sin (3 x)

What is the general solution for (sin(53.3))/(20.7)=(sin(x))/(24.9) ?
The general solution for (sin(53.3))/(20.7)=(sin(x))/(24.9) is x=1.30337…+360n,x=180-1.30337…+360n