Solve 486^circ-tan35^circ/1+tan65^circtan35^circ

$$\frac { 486 ^ { \circ } - \tan 35 ^ { \circ } } { 1 + \tan 65 ^ { \circ } \tan 35 ^ { \circ } }$$

Evaluate

$$\frac{24264989623089514515000000000000000}{125079995574184181786035509056921}\approx 193.995766563$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{486 - 0.7002075382097097}{1 + 2.1445069205095586 \cdot 0.7002075382097097}$$

Subtract 0.7002075382097097 from 486 to get 485.2997924617902903.

$$\frac{485.2997924617902903}{1+2.1445069205095586\times 0.7002075382097097}$$

Multiply 2.1445069205095586 and 0.7002075382097097 to get 1.50159991148368363572071018113842.

$$\frac{485.2997924617902903}{1+1.50159991148368363572071018113842}$$

Add 1 and 1.50159991148368363572071018113842 to get 2.50159991148368363572071018113842.

$$\frac{485.2997924617902903}{2.50159991148368363572071018113842}$$

Expand \frac{485.2997924617902903}{2.50159991148368363572071018113842} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{48529979246179029030000000000000000}{250159991148368363572071018113842}$$

Reduce the fraction \frac{48529979246179029030000000000000000}{250159991148368363572071018113842} to lowest terms by extracting and canceling out 2.

$$\frac{24264989623089514515000000000000000}{125079995574184181786035509056921}$$

Factor

$$\frac{3 \cdot 347 \cdot 1307 \cdot 8009 \cdot 445354141 \cdot 2 ^ {15} \cdot 5 ^ {16}}{41 \cdot 173 \cdot 839 \cdot 15361 \cdot 1368284626319248733443} = 193\frac{1.2455047727196853 \times 10^{32}}{1.2507999557418419 \times 10^{32}} = 193.99576656283216$$