Solve pi/4*(20*10^-2)^2*60*10^-2*7*1450*tan20^circ

$$\frac { \pi } { 4 } \times ( 20 \times 10 ^ { - 2 } ) ^ { 2 } \times 60 \times 10 ^ { - 2 } \times 7 \times 1450 \times \tan 20 ^ { \circ }$$

Evaluate

$$\frac{11082893633405861253\pi }{500000000000000000}\approx 69.635874438$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\pi}{4} \cdot {(20 \cdot 10 ^ {-2})} ^ {2} \cdot 60 \cdot 10 ^ {-2} \cdot 7 \cdot 1450 \cdot 0.36397023426620234$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\pi }{4}\times \left(20\times \frac{1}{100}\right)^{2}\times 60\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Multiply 20 and \frac{1}{100} to get \frac{1}{5}.

$$\frac{\pi }{4}\times \left(\frac{1}{5}\right)^{2}\times 60\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{\pi }{4}\times \frac{1}{25}\times 60\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Multiply \frac{1}{25} and 60 to get \frac{12}{5}.

$$\frac{\pi }{4}\times \frac{12}{5}\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\pi }{4}\times \frac{12}{5}\times \frac{1}{100}\times 7\times 1450\times 0.36397023426620234$$

Multiply \frac{12}{5} and \frac{1}{100} to get \frac{3}{125}.

$$\frac{\pi }{4}\times \frac{3}{125}\times 7\times 1450\times 0.36397023426620234$$

Multiply \frac{3}{125} and 7 to get \frac{21}{125}.

$$\frac{\pi }{4}\times \frac{21}{125}\times 1450\times 0.36397023426620234$$

Multiply \frac{21}{125} and 1450 to get \frac{1218}{5}.

$$\frac{\pi }{4}\times \frac{1218}{5}\times 0.36397023426620234$$

Multiply \frac{1218}{5} and 0.36397023426620234 to get \frac{11082893633405861253}{125000000000000000}.

$$\frac{\pi }{4}\times \frac{11082893633405861253}{125000000000000000}$$

Multiply \frac{\pi }{4} times \frac{11082893633405861253}{125000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\pi \times 11082893633405861253}{4\times 125000000000000000}$$

Multiply 4 and 125000000000000000 to get 500000000000000000.

$$\frac{\pi \times 11082893633405861253}{500000000000000000}$$

Expand

$$\frac{11082893633405861253 \pi}{500000000000000000} = 69\frac{3.1793721922494464 \times 10^{17}}{5 \times 10^{17}} = 69.63587443844989$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\pi}{4} \cdot {(20 \cdot 10 ^ {-2})} ^ {2} \cdot 60 \cdot 10 ^ {-2} \cdot 7 \cdot 1450 \cdot 0.36397023426620234$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\pi }{4}\times \left(20\times \frac{1}{100}\right)^{2}\times 60\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Multiply 20 and \frac{1}{100} to get \frac{1}{5}.

$$\frac{\pi }{4}\times \left(\frac{1}{5}\right)^{2}\times 60\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{\pi }{4}\times \frac{1}{25}\times 60\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Multiply \frac{1}{25} and 60 to get \frac{12}{5}.

$$\frac{\pi }{4}\times \frac{12}{5}\times 10^{-2}\times 7\times 1450\times 0.36397023426620234$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\pi }{4}\times \frac{12}{5}\times \frac{1}{100}\times 7\times 1450\times 0.36397023426620234$$

Multiply \frac{12}{5} and \frac{1}{100} to get \frac{3}{125}.

$$\frac{\pi }{4}\times \frac{3}{125}\times 7\times 1450\times 0.36397023426620234$$

Multiply \frac{3}{125} and 7 to get \frac{21}{125}.

$$\frac{\pi }{4}\times \frac{21}{125}\times 1450\times 0.36397023426620234$$

Multiply \frac{21}{125} and 1450 to get \frac{1218}{5}.

$$\frac{\pi }{4}\times \frac{1218}{5}\times 0.36397023426620234$$

Multiply \frac{1218}{5} and 0.36397023426620234 to get \frac{11082893633405861253}{125000000000000000}.

$$\frac{\pi }{4}\times \frac{11082893633405861253}{125000000000000000}$$

Multiply \frac{\pi }{4} times \frac{11082893633405861253}{125000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\pi \times 11082893633405861253}{4\times 125000000000000000}$$

Multiply 4 and 125000000000000000 to get 500000000000000000.

$$\frac{\pi \times 11082893633405861253}{500000000000000000}$$