Solve 16*1sin(20sin(65))/sin(45)

$$\frac{ 16 \cdot 1 \sin ( 20 \sin ( 65 ) ) }{ \sin ( 45 ) }$$

Evaluate

$$\frac{3111103112816723\sqrt{2}}{625000000000000}\approx 7.039622746$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{16 \cdot 1 \cdot 0.3111103112816723}{\sin(45)}$$

Multiply 16 and 1 to get 16.

$$\frac{16\times 0.3111103112816723}{\sin(45)}$$

Multiply 16 and 0.3111103112816723 to get 4.9777649805067568.

$$\frac{4.9777649805067568}{\sin(45)}$$

Get the value of \sin(45) from trigonometric values table.

$$\frac{4.9777649805067568}{\frac{\sqrt{2}}{2}}$$

Divide 4.9777649805067568 by \frac{\sqrt{2}}{2} by multiplying 4.9777649805067568 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{4.9777649805067568\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{4.9777649805067568\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4.9777649805067568\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{4.9777649805067568\times 2\sqrt{2}}{2}$$

Multiply 4.9777649805067568 and 2 to get 9.9555299610135136.

$$\frac{9.9555299610135136\sqrt{2}}{2}$$

Divide 9.9555299610135136\sqrt{2} by 2 to get 4.9777649805067568\sqrt{2}.

$$4.9777649805067568\sqrt{2}$$