Trigonometry Examples

$\frac{B}{\sin (42)} = \frac{12}{\sin (96)}$

Step 1

Multiply both sides by $\sin (42)$ .

$\frac{B}{\sin (42)} \sin (42) = \frac{12}{\sin (96)} \sin (42)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $\sin (42)$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{B}{\sin (42)} \sin (42) = \frac{12}{\sin (96)} \sin (42)$

Step 2.1.1.2

Rewrite the expression.

$B = \frac{12}{\sin (96)} \sin (42)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{12}{\sin (96)} \sin (42)$ .

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Step 2.2.1.1

Separate fractions.

$B = \frac{12}{1} \cdot \frac{1}{\sin (96)} \sin (42)$

Step 2.2.1.2

Convert from $\frac{1}{\sin (96)}$ to $\csc (96)$ .

$B = \frac{12}{1} \csc (96) \sin (42)$

Step 2.2.1.3

Divide $12$ by $1$ .

$B = 12 \csc (96) \sin (42)$

Step 2.2.1.4

Evaluate $\csc (96)$ .

$B = 12 \cdot 1.00550827 \sin (42)$

Step 2.2.1.5

Multiply $12$ by $1.00550827$ .

$B = 12.06609935 \sin (42)$

Step 2.2.1.6

Evaluate $\sin (42)$ .

$B = 12.06609935 \cdot 0.6691306$

Step 2.2.1.7

Multiply $12.06609935$ by $0.6691306$ .

$B = 8.07379637$