What is the general solution for sin(60)= x/(32) ?

The general solution for sin(60)= x/(32) is x=16sqrt(3)

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sin(60)= x/(32)

sin (6 0^{\circ}) = \frac{x}{32}

x = 163

Decimal

x = 27.71281 \dots

Solution steps

sin (6 0^{\circ}) = \frac{x}{32}

Switch sides

\frac{x}{32} = sin (6 0^{\circ})

Simplify

sin (6 0^{\circ}) : \frac{3}{2}

sin (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

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}

\frac{x}{32} = \frac{3}{2}

Multiply both sides by

32

\frac{x}{32} = \frac{3}{2}

Multiply both sides by

32

\frac{32 x}{32} = \frac{32 3}{2}

Simplify

x = 163

x = 163

What is the general solution for sin(60)= x/(32) ?
The general solution for sin(60)= x/(32) is x=16sqrt(3)