Solve 119*(90.16cos25^circ+T*sin25^circ)+Tcos25^circ=90160sin25^circ

$$119 \times ( 90.16 \cos 25 ^ { \circ } + T \times \sin 25 ^ { \circ } ) + T \cos 25 ^ { \circ } = 90160 \sin 25 ^ { \circ }$$

Solve for T

$$T=-\frac{2157875683420595T_{0}}{119741840826531508}+\frac{168925297494724781353}{299354602066328770}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$119 \cdot {(90.16 \cdot 0.9063077870366499 + T \cdot 0.42261826174069944)} + T 0.9063077870366499 = 90160 \cdot 0.42261826174069944$$

Multiply 90.16 and 0.9063077870366499 to get 81.712710079224354984.

$$119\left(81.712710079224354984+T\times 0.42261826174069944\right)+T_{0}\times 0.9063077870366499=90160\times 0.42261826174069944$$

Use the distributive property to multiply 119 by 81.712710079224354984+T\times 0.42261826174069944.

$$9723.812499427698243096+119T\times 0.42261826174069944+T_{0}\times 0.9063077870366499=90160\times 0.42261826174069944$$

Multiply 119 and 0.42261826174069944 to get 50.29157314714323336.

$$9723.812499427698243096+50.29157314714323336T+T_{0}\times 0.9063077870366499=90160\times 0.42261826174069944$$

Multiply 90160 and 0.42261826174069944 to get 38103.2624785414615104.

$$9723.812499427698243096+50.29157314714323336T+T_{0}\times 0.9063077870366499=38103.2624785414615104$$

Subtract 9723.812499427698243096 from both sides.

$$50.29157314714323336T+T_{0}\times 0.9063077870366499=38103.2624785414615104-9723.812499427698243096$$

Subtract 9723.812499427698243096 from 38103.2624785414615104 to get 28379.449979113763267304.

$$50.29157314714323336T+T_{0}\times 0.9063077870366499=28379.449979113763267304$$

Subtract T_{0}\times 0.9063077870366499 from both sides.

$$50.29157314714323336T=28379.449979113763267304-T_{0}\times 0.9063077870366499$$

Multiply -1 and 0.9063077870366499 to get -0.9063077870366499.

$$50.29157314714323336T=28379.449979113763267304-0.9063077870366499T_{0}$$

The equation is in standard form.

$$50.29157314714323336T=-\frac{9063077870366499T_{0}}{10000000000000000}+28379.449979113763267304$$

Divide both sides of the equation by 50.29157314714323336, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{50.29157314714323336T}{50.29157314714323336}=\frac{-\frac{9063077870366499T_{0}}{10000000000000000}+28379.449979113763267304}{50.29157314714323336}$$

Dividing by 50.29157314714323336 undoes the multiplication by 50.29157314714323336.

$$T=\frac{-\frac{9063077870366499T_{0}}{10000000000000000}+28379.449979113763267304}{50.29157314714323336}$$

Divide 28379.449979113763267304-\frac{9063077870366499T_{0}}{10000000000000000} by 50.29157314714323336 by multiplying 28379.449979113763267304-\frac{9063077870366499T_{0}}{10000000000000000} by the reciprocal of 50.29157314714323336.

$$T=-\frac{2157875683420595T_{0}}{119741840826531508}+\frac{168925297494724781353}{299354602066328770}$$

Solve for T_0

$$T_{0}=-\frac{119741840826531508T}{2157875683420595}+\frac{337850594989449562706}{10789378417102975}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$119 \cdot {(90.16 \cdot 0.9063077870366499 + T \cdot 0.42261826174069944)} + T 0.9063077870366499 = 90160 \cdot 0.42261826174069944$$

Multiply 90.16 and 0.9063077870366499 to get 81.712710079224354984.

$$119\left(81.712710079224354984+T\times 0.42261826174069944\right)+T_{0}\times 0.9063077870366499=90160\times 0.42261826174069944$$

Use the distributive property to multiply 119 by 81.712710079224354984+T\times 0.42261826174069944.

$$9723.812499427698243096+119T\times 0.42261826174069944+T_{0}\times 0.9063077870366499=90160\times 0.42261826174069944$$

Multiply 119 and 0.42261826174069944 to get 50.29157314714323336.

$$9723.812499427698243096+50.29157314714323336T+T_{0}\times 0.9063077870366499=90160\times 0.42261826174069944$$

Multiply 90160 and 0.42261826174069944 to get 38103.2624785414615104.

$$9723.812499427698243096+50.29157314714323336T+T_{0}\times 0.9063077870366499=38103.2624785414615104$$

Subtract 9723.812499427698243096 from both sides.

$$50.29157314714323336T+T_{0}\times 0.9063077870366499=38103.2624785414615104-9723.812499427698243096$$

Subtract 9723.812499427698243096 from 38103.2624785414615104 to get 28379.449979113763267304.

$$50.29157314714323336T+T_{0}\times 0.9063077870366499=28379.449979113763267304$$

Subtract 50.29157314714323336T from both sides.

$$T_{0}\times 0.9063077870366499=28379.449979113763267304-50.29157314714323336T$$

The equation is in standard form.

$$0.9063077870366499T_{0}=-\frac{628644664339290417T}{12500000000000000}+28379.449979113763267304$$

Divide both sides of the equation by 0.9063077870366499, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.9063077870366499T_{0}}{0.9063077870366499}=\frac{-\frac{628644664339290417T}{12500000000000000}+28379.449979113763267304}{0.9063077870366499}$$

Dividing by 0.9063077870366499 undoes the multiplication by 0.9063077870366499.

$$T_{0}=\frac{-\frac{628644664339290417T}{12500000000000000}+28379.449979113763267304}{0.9063077870366499}$$

Divide 28379.449979113763267304-\frac{628644664339290417T}{12500000000000000} by 0.9063077870366499 by multiplying 28379.449979113763267304-\frac{628644664339290417T}{12500000000000000} by the reciprocal of 0.9063077870366499.

$$T_{0}=-\frac{119741840826531508T}{2157875683420595}+\frac{337850594989449562706}{10789378417102975}$$