Solve 16*1sin20^circ*sin75^circ/sin45^circ

$$\frac { 16 \cdot 1 \sin 20 ^ { \circ } \cdot \sin 75 ^ { \circ } } { \sin 45 ^ { \circ } }$$

Evaluate

$$\frac{3308193876986619\sqrt{2}}{625000000000000}\approx 7.485588236$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{16 \cdot 1 \cdot 0.3308193876986619}{\sin(45)}$$

Multiply 16 and 1 to get 16.

$$\frac{16\times 0.3308193876986619}{\sin(45)}$$

Multiply 16 and 0.3308193876986619 to get 5.2931102031785904.

$$\frac{5.2931102031785904}{\sin(45)}$$

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

$$\frac{5.2931102031785904}{\frac{\sqrt{2}}{2}}$$

Divide 5.2931102031785904 by \frac{\sqrt{2}}{2} by multiplying 5.2931102031785904 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{5.2931102031785904\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{5.2931102031785904\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5.2931102031785904\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5.2931102031785904\times 2\sqrt{2}}{2}$$

Multiply 5.2931102031785904 and 2 to get 10.5862204063571808.

$$\frac{10.5862204063571808\sqrt{2}}{2}$$

Divide 10.5862204063571808\sqrt{2} by 2 to get 5.2931102031785904\sqrt{2}.

$$5.2931102031785904\sqrt{2}$$