Solve 700/sin124=a/sin21^circ

$$\frac { 700 } { \sin 124 } = \frac { a } { \sin 21 ^ { \circ } }$$

Solve for a

$$a = \frac{2508575646817101890}{8290375725550417} = 302\frac{4882177700875890}{8290375725550417} \approx 302.588897037$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{700}{0.8290375725550417} = \frac{a}{0.35836794954530027}$$

Expand \frac{700}{0.8290375725550417} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{7000000000000000000}{8290375725550417}=\frac{a}{0.35836794954530027}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{a}{0.35836794954530027}=\frac{7000000000000000000}{8290375725550417}$$

Multiply both sides by 0.35836794954530027.

$$a=\frac{7000000000000000000}{8290375725550417}\times 0.35836794954530027$$

Convert decimal number 0.35836794954530027 to fraction \frac{35836794954530027}{10000000000}. Reduce the fraction \frac{35836794954530027}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{7000000000000000000}{8290375725550417}\times \frac{35836794954530027}{100000000000000000}$$

Multiply \frac{7000000000000000000}{8290375725550417} times \frac{35836794954530027}{100000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{7000000000000000000\times 35836794954530027}{8290375725550417\times 100000000000000000}$$

Do the multiplications in the fraction \frac{7000000000000000000\times 35836794954530027}{8290375725550417\times 100000000000000000}.

$$a=\frac{250857564681710189000000000000000000}{829037572555041700000000000000000}$$

Reduce the fraction \frac{250857564681710189000000000000000000}{829037572555041700000000000000000} to lowest terms by extracting and canceling out 100000000000000000.

$$a=\frac{2508575646817101890}{8290375725550417}$$