Solve 26^2/270*cos65^circ

$$\frac { 26 ^ { 2 } } { 270 } \times \cos 65 ^ { \circ }$$

Evaluate

$$\frac{297593692642409189}{281250000000000000}\approx 1.058110907$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{26 ^ {2}}{270} \cdot 0.42261826174069944$$

Calculate 26 to the power of 2 and get 676.

$$\frac{676}{270}\times 0.42261826174069944$$

Reduce the fraction \frac{676}{270} to lowest terms by extracting and canceling out 2.

$$\frac{338}{135}\times 0.42261826174069944$$

Convert decimal number 0.42261826174069944 to fraction \frac{5282728271758743}{10000000000}. Reduce the fraction \frac{5282728271758743}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{338}{135}\times \frac{5282728271758743}{12500000000000000}$$

Multiply \frac{338}{135} times \frac{5282728271758743}{12500000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{338\times 5282728271758743}{135\times 12500000000000000}$$

Do the multiplications in the fraction \frac{338\times 5282728271758743}{135\times 12500000000000000}.

$$\frac{1785562155854455134}{1687500000000000000}$$

Reduce the fraction \frac{1785562155854455134}{1687500000000000000} to lowest terms by extracting and canceling out 6.

$$\frac{297593692642409189}{281250000000000000}$$

Factor

$$\frac{101 \cdot 55843 \cdot 24016159 \cdot 13 ^ {3}}{2 ^ {13} \cdot 3 ^ {2} \cdot 5 ^ {18}} = 1\frac{16343692642409216}{2.8125 \times 10^{17}} = 1.0581109071730106$$