What is the general solution for (sin(115))/(20)=(sin(B))/(15) ?

The general solution for (sin(115))/(20)=(sin(B))/(15) is B=0.74739…+360n,B=180-0.74739…+360n

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Popular >

(sin(115))/(20)=(sin(B))/(15)

Solution

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

Solution

B = 0.74739 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.74739 \dots + 36 0^{\circ} n

Radians

B = 0.74739 \dots + 2 πn, B = π - 0.74739 \dots + 2 πn

Solution steps

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

Switch sides

\frac{sin ( B )}{15} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiply both sides by

10

\frac{sin ( B )}{15} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiply both sides by

10

\frac{sin ( B )}{15} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplify

\frac{sin ( B )}{15} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplify

\frac{sin ( B )}{15} \cdot 10 : \frac{2 sin ( B )}{3}

\frac{sin ( B )}{15} \cdot 10

Multiply fractions:

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

= \frac{sin ( B ) \cdot 10}{15}

Cancel the common factor:

5

= \frac{2 sin ( B )}{3}

Simplify

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10 : \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Multiply fractions:

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

= \frac{sin ( 11 5 ^{\circ} ) \cdot 10}{20}

Cancel the common factor:

10

= \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiply both sides by

3

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiply both sides by

3

\frac{3 \cdot 2 sin ( B )}{3} = \frac{3 sin ( 11 5 ^{\circ} )}{2}

Simplify

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

Divide both sides by

2

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

Divide both sides by

2

\frac{2 sin ( B )}{2} = \frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

Simplify

\frac{2 sin ( B )}{2} = \frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

Simplify

\frac{2 sin ( B )}{2} : sin (B)

\frac{2 sin ( B )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sin (B)

Simplify

\frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2} : \frac{3 sin ( 11 5 ^{\circ} )}{4}

\frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

Apply the fraction rule:

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

= \frac{3 sin ( 11 5 ^{\circ} )}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

Apply trig inverse properties

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

General solutions for

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

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

B = arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n

B = arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n

Show solutions in decimal form

B = 0.74739 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.74739 \dots + 36 0^{\circ} n

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Frequently Asked Questions (FAQ)

What is the general solution for (sin(115))/(20)=(sin(B))/(15) ?
The general solution for (sin(115))/(20)=(sin(B))/(15) is B=0.74739…+360n,B=180-0.74739…+360n