Trigonometry Examples

$\frac{b}{\sin (114.2)} = \frac{400}{\sin (42.12)}$

Step 1

Multiply both sides of the equation by $\sin (114.2)$ .

$\sin (114.2) \frac{b}{\sin (114.2)} = \sin (114.2) \frac{400}{\sin (42.12)}$

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $\sin (114.2)$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor.

$\sin (114.2) \frac{b}{\sin (114.2)} = \sin (114.2) \frac{400}{\sin (42.12)}$

Step 2.1.1.2

Rewrite the expression.

$b = \sin (114.2) \frac{400}{\sin (42.12)}$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $\sin (114.2) \frac{400}{\sin (42.12)}$ .

Tap for more steps...

Step 2.2.1.1

Separate fractions.

$b = \sin (114.2) (\frac{400}{1} \cdot \frac{1}{\sin (42.12)})$

Step 2.2.1.2

Convert from $\frac{1}{\sin (42.12)}$ to $\csc (42.12)$ .

$b = \sin (114.2) (\frac{400}{1} \csc (42.12))$

Step 2.2.1.3

Divide $400$ by $1$ .

$b = \sin (114.2) (400 \csc (42.12))$

Step 2.2.1.4

Move $400$ to the left of $\sin (114.2)$ .

$b = 400 \sin (114.2) \csc (42.12)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = 400 \sin (114.2) \csc (42.12)$

Decimal Form:

$b = 543.99268335 \dots$