Solve 100*sin^245/20

$$\frac { 100 \times \sin ^ { 2 } 45 } { 20 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

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

$$\frac{100\times \left(\frac{\sqrt{2}}{2}\right)^{2}}{20}$$

To raise \frac{\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{100\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{20}$$

Express 100\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{\frac{100\left(\sqrt{2}\right)^{2}}{2^{2}}}{20}$$

Express \frac{\frac{100\left(\sqrt{2}\right)^{2}}{2^{2}}}{20} as a single fraction.

$$\frac{100\left(\sqrt{2}\right)^{2}}{2^{2}\times 20}$$

Cancel out 20 in both numerator and denominator.

$$\frac{5\left(\sqrt{2}\right)^{2}}{2^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\times 2}{2^{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{10}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}$$