Solve 5*frac{4^2/2/tan(frac{360{2*5})}}{2}

$$\frac{ 5 \cdot \frac{ \frac{ { 4 }^{ 2 } }{ 2 } }{ \tan ( \frac{ 360 }{ 2 \cdot 5 } ) } }{ 2 }$$

Evaluate

$$\frac{25000000000000000}{908178160006701}\approx 27.527638409$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{5 \cdot \frac{\frac{{(4)} ^ {2}}{2}}{0.7265425280053608}}{2}$$

Express \frac{\frac{4^{2}}{2}}{0.7265425280053608} as a single fraction.

$$\frac{5\times \frac{4^{2}}{2\times 0.7265425280053608}}{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{5\times \frac{16}{2\times 0.7265425280053608}}{2}$$

Multiply 2 and 0.7265425280053608 to get 1.4530850560107216.

$$\frac{5\times \frac{16}{1.4530850560107216}}{2}$$

Expand \frac{16}{1.4530850560107216} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{5\times \frac{160000000000000000}{14530850560107216}}{2}$$

Reduce the fraction \frac{160000000000000000}{14530850560107216} to lowest terms by extracting and canceling out 16.

$$\frac{5\times \frac{10000000000000000}{908178160006701}}{2}$$

Express 5\times \frac{10000000000000000}{908178160006701} as a single fraction.

$$\frac{\frac{5\times 10000000000000000}{908178160006701}}{2}$$

Multiply 5 and 10000000000000000 to get 50000000000000000.

$$\frac{\frac{50000000000000000}{908178160006701}}{2}$$

Express \frac{\frac{50000000000000000}{908178160006701}}{2} as a single fraction.

$$\frac{50000000000000000}{908178160006701\times 2}$$

Multiply 908178160006701 and 2 to get 1816356320013402.

$$\frac{50000000000000000}{1816356320013402}$$

Reduce the fraction \frac{50000000000000000}{1816356320013402} to lowest terms by extracting and canceling out 2.

$$\frac{25000000000000000}{908178160006701}$$

Factor

$$\frac{2 ^ {15} \cdot 5 ^ {17}}{100908684445189 \cdot 3 ^ {2}} = 27\frac{479189679819073}{908178160006701} = 27.527638409423474$$