Solve h=frac{800sin44^{circ}sin31^{circ}}{sin31^circsin46^circ+sin59^circsin44^circ}

$$h = \frac { 800 \sin 44 ^ { \circ } \sin 31 ^ { \circ } } { \sin 31 ^ { \circ } \sin 46 ^ { \circ } + \sin 59 ^ { \circ } \sin 44 ^ { \circ } }$$

Solve for h

$$h = \frac{2385170065609048219763777471024400}{8049381885742235082558365499889} = 296\frac{2.553027429346663 \times 10^{30}}{8.049381885742234 \times 10^{30}} \approx 296.317170618$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$h = \frac{800 \cdot 0.6946583704589973 \cdot 0.5150380749100542}{0.5150380749100542 \cdot 0.7193398003386511 + 0.8571673007021122 \cdot 0.6946583704589973}$$

Multiply 800 and 0.6946583704589973 to get 555.72669636719784.

$$h=\frac{555.72669636719784\times 0.5150380749100542}{0.5150380749100542\times 0.7193398003386511+0.8571673007021122\times 0.6946583704589973}$$

Multiply 555.72669636719784 and 0.5150380749100542 to get 286.220407873085786371653296522928.

$$h=\frac{286.220407873085786371653296522928}{0.5150380749100542\times 0.7193398003386511+0.8571673007021122\times 0.6946583704589973}$$

Multiply 0.5150380749100542 and 0.7193398003386511 to get 0.37048738597260161682733225588962.

$$h=\frac{286.220407873085786371653296522928}{0.37048738597260161682733225588962+0.8571673007021122\times 0.6946583704589973}$$

Multiply 0.8571673007021122 and 0.6946583704589973 to get 0.59543844031646659307967160409706.

$$h=\frac{286.220407873085786371653296522928}{0.37048738597260161682733225588962+0.59543844031646659307967160409706}$$

Add 0.37048738597260161682733225588962 and 0.59543844031646659307967160409706 to get 0.96592582628906820990700385998668.

$$h=\frac{286.220407873085786371653296522928}{0.96592582628906820990700385998668}$$

Expand \frac{286.220407873085786371653296522928}{0.96592582628906820990700385998668} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$h=\frac{28622040787308578637165329652292800}{96592582628906820990700385998668}$$

Reduce the fraction \frac{28622040787308578637165329652292800}{96592582628906820990700385998668} to lowest terms by extracting and canceling out 12.

$$h=\frac{2385170065609048219763777471024400}{8049381885742235082558365499889}$$

Assign h

$$h≔\frac{2385170065609048219763777471024400}{8049381885742235082558365499889}$$