Solve 15+10cos19-13cos26/10sin19+13sin26

$$\frac { 15 + 10 \cos 19 - 13 \cos 26 } { 10 \sin 19 + 13 \sin 26 }$$

Evaluate

$$\frac{63854315770519985}{44772532264147863}\approx 1.426193975$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{15 + 10 \cdot 0.9455185755993168 - 13 \cdot 0.898794046299167}{10 \cdot 0.32556815445715664 + 13 \cdot 0.4383711467890774}$$

Multiply 10 and 0.9455185755993168 to get 9.455185755993168.

$$\frac{15+9.455185755993168-13\times 0.898794046299167}{10\times 0.32556815445715664+13\times 0.4383711467890774}$$

Add 15 and 9.455185755993168 to get 24.455185755993168.

$$\frac{24.455185755993168-13\times 0.898794046299167}{10\times 0.32556815445715664+13\times 0.4383711467890774}$$

Multiply 13 and 0.898794046299167 to get 11.684322601889171.

$$\frac{24.455185755993168-11.684322601889171}{10\times 0.32556815445715664+13\times 0.4383711467890774}$$

Subtract 11.684322601889171 from 24.455185755993168 to get 12.770863154103997.

$$\frac{12.770863154103997}{10\times 0.32556815445715664+13\times 0.4383711467890774}$$

Multiply 10 and 0.32556815445715664 to get 3.2556815445715664.

$$\frac{12.770863154103997}{3.2556815445715664+13\times 0.4383711467890774}$$

Multiply 13 and 0.4383711467890774 to get 5.6988249082580062.

$$\frac{12.770863154103997}{3.2556815445715664+5.6988249082580062}$$

Add 3.2556815445715664 and 5.6988249082580062 to get 8.9545064528295726.

$$\frac{12.770863154103997}{8.9545064528295726}$$

Expand \frac{12.770863154103997}{8.9545064528295726} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{127708631541039970}{89545064528295726}$$

Reduce the fraction \frac{127708631541039970}{89545064528295726} to lowest terms by extracting and canceling out 2.

$$\frac{63854315770519985}{44772532264147863}$$

Factor

$$\frac{5 \cdot 19 \cdot 331 \cdot 2030666744173}{3 \cdot 7 \cdot 1979 \cdot 2267 \cdot 475220371} = 1\frac{19081783506372120}{44772532264147864} \approx 1.426193975$$