Solve 485^circ-tan35/1+tan65^circtan35

$$\frac { 485 ^ { \circ } - \tan 35 } { 1 + \tan 65 ^ { \circ } \tan 35 }$$

Evaluate

$$\frac{24214989623089514515000000000000000}{125079995574184181786035509056921}\approx 193.596022385$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{485 - 0.7002075382097097}{1 + 2.1445069205095586 \cdot 0.7002075382097097}$$

Subtract 0.7002075382097097 from 485 to get 484.2997924617902903.

$$\frac{484.2997924617902903}{1+2.1445069205095586\times 0.7002075382097097}$$

Multiply 2.1445069205095586 and 0.7002075382097097 to get 1.50159991148368363572071018113842.

$$\frac{484.2997924617902903}{1+1.50159991148368363572071018113842}$$

Add 1 and 1.50159991148368363572071018113842 to get 2.50159991148368363572071018113842.

$$\frac{484.2997924617902903}{2.50159991148368363572071018113842}$$

Expand \frac{484.2997924617902903}{2.50159991148368363572071018113842} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{48429979246179029030000000000000000}{250159991148368363572071018113842}$$

Reduce the fraction \frac{48429979246179029030000000000000000}{250159991148368363572071018113842} to lowest terms by extracting and canceling out 2.

$$\frac{24214989623089514515000000000000000}{125079995574184181786035509056921}$$

Factor

$$\frac{7 \cdot 59 \cdot 1139807 \cdot 10288046333 \cdot 2 ^ {15} \cdot 5 ^ {16}}{41 \cdot 173 \cdot 839 \cdot 15361 \cdot 1368284626319248733443} = 193\frac{7.455047727196874 \times 10^{31}}{1.2507999557418419 \times 10^{32}} = 193.59602238495248$$