What is the general solution for (35)/(sin(A))=(60)/(sin(25)) ?

The general solution for (35)/(sin(A))=(60)/(sin(25)) is A=0.24909…+360n,A=180-0.24909…+360n

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(35)/(sin(A))=(60)/(sin(25))

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

A = 0.24909 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.24909 \dots + 36 0^{\circ} n

Radians

A = 0.24909 \dots + 2 πn, A = π - 0.24909 \dots + 2 πn

Solution steps

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

Cross multiply

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

35 sin (2 5^{\circ}) = sin (A) \cdot 60

35 sin (2 5^{\circ}) = sin (A) \cdot 60

Switch sides

sin (A) \cdot 60 = 35 sin (2 5^{\circ})

Divide both sides by

60

sin (A) \cdot 60 = 35 sin (2 5^{\circ})

Divide both sides by

60

\frac{sin ( A ) \cdot 60}{60} = \frac{35 sin ( 2 5 ^{\circ} )}{60}

Simplify

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

Verify Solutions

Find undefined (singularity) points:

sin (A) = 0

Take the denominator(s) of

\frac{35}{sin ( A )}

and compare to zero

sin (A) = 0

The following points are undefined

sin (A) = 0

Combine undefined points with solutions:

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

Apply trig inverse properties

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

General solutions for

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

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

A = arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n

A = arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n

Show solutions in decimal form

A = 0.24909 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.24909 \dots + 36 0^{\circ} n

4 csc (x) + sin (x) + 5 = 0

tan (x) = 1087

- 3 sin (3 x) = 1

\frac{1}{cos ( x ) - cos ( x )} = sin (x) tan (x)

cos (θ) = \frac{3}{5} (270360)

What is the general solution for (35)/(sin(A))=(60)/(sin(25)) ?
The general solution for (35)/(sin(A))=(60)/(sin(25)) is A=0.24909…+360n,A=180-0.24909…+360n