Solve 6378100(1-0.082108005)/(1-0.082108005*sin^230^circ)

$$\frac { 6378100 ( 1 - 0.082108005 ) } { ( 1 - 0.082108005 \times \sin ^ { 2 } 30 ^ { \circ } ) }$$

Evaluate

$$\frac{4683525546647600}{783578399}\approx 5977098.848851243$$

Solution Steps

Subtract 0.082108005 from 1 to get 0.917891995.

$$\frac{6378100\times 0.917891995}{1-0.082108005\left(\sin(30)\right)^{2}}$$

Multiply 6378100 and 0.917891995 to get 5854406.9333095.

$$\frac{5854406.9333095}{1-0.082108005\left(\sin(30)\right)^{2}}$$

Get the value of \sin(30) from trigonometric values table.

$$\frac{5854406.9333095}{1-0.082108005\times \left(\frac{1}{2}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{5854406.9333095}{1-0.082108005\times \frac{1}{4}}$$

Multiply 0.082108005 and \frac{1}{4} to get \frac{16421601}{800000000}.

$$\frac{5854406.9333095}{1-\frac{16421601}{800000000}}$$

Subtract \frac{16421601}{800000000} from 1 to get \frac{783578399}{800000000}.

$$\frac{5854406.9333095}{\frac{783578399}{800000000}}$$

Divide 5854406.9333095 by \frac{783578399}{800000000} by multiplying 5854406.9333095 by the reciprocal of \frac{783578399}{800000000}.

$$5854406.9333095\times \frac{800000000}{783578399}$$

Multiply 5854406.9333095 and \frac{800000000}{783578399} to get \frac{4683525546647600}{783578399}.

$$\frac{4683525546647600}{783578399}$$