Solve 84sin69^circ/126+84cos69^circ

$$\frac { 84 \sin 69 ^ { \circ } } { 126 + 84 \cos 69 ^ { \circ } }$$

Evaluate

$$\frac{9335804264972017}{18583679495453004}\approx 0.50236576$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{84 \cdot 0.9335804264972017}{126 + 84 \cdot 0.3583679495453004}$$

Multiply 84 and 0.9335804264972017 to get 78.4207558257649428.

$$\frac{78.4207558257649428}{126+84\times 0.3583679495453004}$$

Multiply 84 and 0.3583679495453004 to get 30.1029077618052336.

$$\frac{78.4207558257649428}{126+30.1029077618052336}$$

Add 126 and 30.1029077618052336 to get 156.1029077618052336.

$$\frac{78.4207558257649428}{156.1029077618052336}$$

Expand \frac{78.4207558257649428}{156.1029077618052336} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{784207558257649428}{1561029077618052336}$$

Reduce the fraction \frac{784207558257649428}{1561029077618052336} to lowest terms by extracting and canceling out 84.

$$\frac{9335804264972017}{18583679495453004}$$

Factor

$$\frac{7 \cdot 269 \cdot 4957941723299}{373 \cdot 1383949917743 \cdot 2 ^ {2} \cdot 3 ^ {2}} = 0.5023657595502694$$