solvefor b,(sin(65)}{14}=\frac{sin(b))/9

Solution

solvefor

b = 0.62195 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.62195 \dots + 36 0^{\circ} n

Radians

b = 0.62195 \dots + 2 πn, b = π - 0.62195 \dots + 2 πn

Solution steps

\frac{sin ( 6 5 ^{\circ} )}{14} = \frac{sin ( b )}{9}

Switch sides

\frac{sin ( b )}{9} = \frac{sin ( 6 5 ^{\circ} )}{14}

Multiply both sides by

9

\frac{sin ( b )}{9} = \frac{sin ( 6 5 ^{\circ} )}{14}

Multiply both sides by

9

\frac{9 sin ( b )}{9} = \frac{9 sin ( 6 5 ^{\circ} )}{14}

Simplify

sin (b) = \frac{9 sin ( 6 5 ^{\circ} )}{14}

sin (b) = \frac{9 sin ( 6 5 ^{\circ} )}{14}

Apply trig inverse properties

sin (b) = \frac{9 sin ( 6 5 ^{\circ} )}{14}

General solutions for

sin (b) = \frac{9 sin ( 6 5 ^{\circ} )}{14}

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

b = arcsin (\frac{9 sin ( 6 5 ^{\circ} )}{14}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{9 sin ( 6 5 ^{\circ} )}{14}) + 36 0^{\circ} n

b = arcsin (\frac{9 sin ( 6 5 ^{\circ} )}{14}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{9 sin ( 6 5 ^{\circ} )}{14}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.62195 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.62195 \dots + 36 0^{\circ} n