Solve sqrt{{left(80/2-30sin(22.5)right)}^2}+{left(100/2-30cos(22.5)right)}^2+60^2

$$\sqrt{ { \left( \frac{ 80 }{ 2 } -30 \sin ( 22.5 ) \right) }^{ 2 } } + { \left( \frac{ 100 }{ 2 } -30 \cos ( 22.5 ) \right) }^{ 2 } + { 60 }^{ 2 }$$

Evaluate

$$4125.078951029133498640156600637201$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt{{(\frac{80}{2} - 30 \cdot 0.3826834323650898)} ^ {2}} + {(\frac{100}{2} - 30 \cdot 0.9238795325112867)} ^ {2} + {(60)} ^ {2}$$

Divide 80 by 2 to get 40.

$$\sqrt{\left(40-30\times 0.3826834323650898\right)^{2}}+\left(\frac{100}{2}-30\times 0.9238795325112867\right)^{2}+60^{2}$$

Multiply 30 and 0.3826834323650898 to get 11.480502970952694.

$$\sqrt{\left(40-11.480502970952694\right)^{2}}+\left(\frac{100}{2}-30\times 0.9238795325112867\right)^{2}+60^{2}$$

Subtract 11.480502970952694 from 40 to get 28.519497029047306.

$$\sqrt{28.519497029047306^{2}}+\left(\frac{100}{2}-30\times 0.9238795325112867\right)^{2}+60^{2}$$

Calculate 28.519497029047306 to the power of 2 and get 813.361710789838113493909985857636.

$$\sqrt{813.361710789838113493909985857636}+\left(\frac{100}{2}-30\times 0.9238795325112867\right)^{2}+60^{2}$$

Calculate the square root of 813.361710789838113493909985857636 and get 28.519497029047306.

$$28.519497029047306+\left(\frac{100}{2}-30\times 0.9238795325112867\right)^{2}+60^{2}$$

Divide 100 by 2 to get 50.

$$28.519497029047306+\left(50-30\times 0.9238795325112867\right)^{2}+60^{2}$$

Multiply 30 and 0.9238795325112867 to get 27.716385975338601.

$$28.519497029047306+\left(50-27.716385975338601\right)^{2}+60^{2}$$

Subtract 27.716385975338601 from 50 to get 22.283614024661399.

$$28.519497029047306+22.283614024661399^{2}+60^{2}$$

Calculate 22.283614024661399 to the power of 2 and get 496.559454000086192640156600637201.

$$28.519497029047306+496.559454000086192640156600637201+60^{2}$$

Add 28.519497029047306 and 496.559454000086192640156600637201 to get 525.078951029133498640156600637201.

$$525.078951029133498640156600637201+60^{2}$$

Calculate 60 to the power of 2 and get 3600.

$$525.078951029133498640156600637201+3600$$

Add 525.078951029133498640156600637201 and 3600 to get 4125.078951029133498640156600637201.

$$4125.078951029133498640156600637201$$