Solve 80^2*sin(45)*sin(45)div2div10

$${ 80 }^{ 2 } \times \sin ( 45 ) \times \sin ( 45 ) \div 2 \div 10$$

Evaluate

$$160$$

Solution Steps

Multiply \sin(45) and \sin(45) to get \left(\sin(45)\right)^{2}.

$$\frac{\frac{80^{2}\left(\sin(45)\right)^{2}}{2}}{10}$$

Express \frac{\frac{80^{2}\left(\sin(45)\right)^{2}}{2}}{10} as a single fraction.

$$\frac{80^{2}\left(\sin(45)\right)^{2}}{2\times 10}$$

Calculate 80 to the power of 2 and get 6400.

$$\frac{6400\left(\sin(45)\right)^{2}}{2\times 10}$$

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

$$\frac{6400\times \left(\frac{\sqrt{2}}{2}\right)^{2}}{2\times 10}$$

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

$$\frac{6400\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}}{2\times 10}$$

Express 6400\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{\frac{6400\left(\sqrt{2}\right)^{2}}{2^{2}}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{\frac{6400\left(\sqrt{2}\right)^{2}}{2^{2}}}{20}$$

Express \frac{\frac{6400\left(\sqrt{2}\right)^{2}}{2^{2}}}{20} as a single fraction.

$$\frac{6400\left(\sqrt{2}\right)^{2}}{2^{2}\times 20}$$

Cancel out 20 in both numerator and denominator.

$$\frac{320\left(\sqrt{2}\right)^{2}}{2^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{320\times 2}{2^{2}}$$

Multiply 320 and 2 to get 640.

$$\frac{640}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{640}{4}$$

Divide 640 by 4 to get 160.

$$160$$