Solve sin80^circ/2cos45^circ=

$$\frac { \sin 80 ^ { \circ } } { 2 \cos 45 ^ { \circ } } =$$

Evaluate

$$\frac{61550484563263\sqrt{2}}{125000000000000}\approx 0.69636424$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.984807753012208}{2 \cos(45)}$$

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

$$\frac{0.984807753012208}{2\times \frac{\sqrt{2}}{2}}$$

Cancel out 2 and 2.

$$\frac{0.984807753012208}{\sqrt{2}}$$

Rationalize the denominator of \frac{0.984807753012208}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{0.984807753012208\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{0.984807753012208\sqrt{2}}{2}$$

Divide 0.984807753012208\sqrt{2} by 2 to get 0.492403876506104\sqrt{2}.

$$0.492403876506104\sqrt{2}$$