Solve 25^2*(sin45^circ)^2/2*9.8

$$\frac { 25 ^ { 2 } \times ( \sin 45 ^ { \circ } ) ^ { 2 } } { 2 \times 9.8 }$$

Evaluate

$$\frac{3125}{196}\approx 15.943877551$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\frac{625\left(\sin(45)\right)^{2}}{2\times 9.8}$$

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

$$\frac{625\times \left(\frac{\sqrt{2}}{2}\right)^{2}}{2\times 9.8}$$

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

$$\frac{625\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{2\times 9.8}$$

Express 625\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{\frac{625\left(\sqrt{2}\right)^{2}}{2^{2}}}{2\times 9.8}$$

Multiply 2 and 9.8 to get 19.6.

$$\frac{\frac{625\left(\sqrt{2}\right)^{2}}{2^{2}}}{19.6}$$

Express \frac{\frac{625\left(\sqrt{2}\right)^{2}}{2^{2}}}{19.6} as a single fraction.

$$\frac{625\left(\sqrt{2}\right)^{2}}{2^{2}\times 19.6}$$

The square of \sqrt{2} is 2.

$$\frac{625\times 2}{2^{2}\times 19.6}$$

Multiply 625 and 2 to get 1250.

$$\frac{1250}{2^{2}\times 19.6}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1250}{4\times 19.6}$$

Multiply 4 and 19.6 to get 78.4.

$$\frac{1250}{78.4}$$

Expand \frac{1250}{78.4} by multiplying both numerator and the denominator by 10.

$$\frac{12500}{784}$$

Reduce the fraction \frac{12500}{784} to lowest terms by extracting and canceling out 4.

$$\frac{3125}{196}$$