Precalculus Examples

$\frac{16}{\sin (82)} = \frac{c}{\sin (57)}$

Step 1

Rewrite the equation as $\frac{c}{\sin (57)} = \frac{16}{\sin (82)}$ .

$\frac{c}{\sin (57)} = \frac{16}{\sin (82)}$

Step 2

Multiply both sides of the equation by $\sin (57)$ .

$\sin (57) \frac{c}{\sin (57)} = \sin (57) \frac{16}{\sin (82)}$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $\sin (57)$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\sin (57) \frac{c}{\sin (57)} = \sin (57) \frac{16}{\sin (82)}$

Step 3.1.1.2

Rewrite the expression.

$c = \sin (57) \frac{16}{\sin (82)}$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $\sin (57) \frac{16}{\sin (82)}$ .

Tap for more steps...

Step 3.2.1.1

Evaluate $\sin (57)$ .

$c = 0.83867056 \frac{16}{\sin (82)}$

Step 3.2.1.2

Separate fractions.

$c = 0.83867056 (\frac{16}{1} \cdot \frac{1}{\sin (82)})$

Step 3.2.1.3

Convert from $\frac{1}{\sin (82)}$ to $\csc (82)$ .

$c = 0.83867056 (\frac{16}{1} \csc (82))$

Step 3.2.1.4

Divide $16$ by $1$ .

$c = 0.83867056 (16 \csc (82))$

Step 3.2.1.5

Evaluate $\csc (82)$ .

$c = 0.83867056 (16 \cdot 1.00982757)$

Step 3.2.1.6

Multiply $0.83867056 (16 \cdot 1.00982757)$ .

Tap for more steps...

Step 3.2.1.6.1

Multiply $16$ by $1.00982757$ .

$c = 0.83867056 \cdot 16.15724116$

Step 3.2.1.6.2

Multiply $0.83867056$ by $16.15724116$ .

$c = 13.55060262$