Solve a/sin35^circ=10/sin40^circ

$$\frac { a } { \sin 35 ^ { \circ } } = \frac { 10 } { \sin 40 ^ { \circ } }$$

Solve for a

$$a = \frac{57357643635104600}{6427876096865393} = 8\frac{5934634860181456}{6427876096865393} \approx 8.923265286$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{a}{0.573576436351046} = \frac{10}{0.6427876096865393}$$

Expand \frac{10}{0.6427876096865393} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{a}{0.573576436351046}=\frac{100000000000000000}{6427876096865393}$$

Multiply both sides by 0.573576436351046.

$$a=\frac{100000000000000000}{6427876096865393}\times 0.573576436351046$$

Convert decimal number 0.573576436351046 to fraction \frac{286788218175523}{10000000000}. Reduce the fraction \frac{286788218175523}{10000000000} to lowest terms by extracting and canceling out 1.

$$a=\frac{100000000000000000}{6427876096865393}\times \frac{286788218175523}{500000000000000}$$

Multiply \frac{100000000000000000}{6427876096865393} times \frac{286788218175523}{500000000000000} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{100000000000000000\times 286788218175523}{6427876096865393\times 500000000000000}$$

Do the multiplications in the fraction \frac{100000000000000000\times 286788218175523}{6427876096865393\times 500000000000000}.

$$a=\frac{28678821817552300000000000000000}{3213938048432696500000000000000}$$

Reduce the fraction \frac{28678821817552300000000000000000}{3213938048432696500000000000000} to lowest terms by extracting and canceling out 500000000000000.

$$a=\frac{57357643635104600}{6427876096865393}$$