x^2+152.5^2=163.88^2+(x+60)^2-2(163.88)(x+60)\cos (68.52)

asked by guest
on Jan 12, 2025 at 9:12 pm



You asked:

Solve the equation \({x}^{2} + {152.5}^{2} = {163.88}^{2} + {\left( x + 60 \right)}^{2} - 2 \cdot 163.88 \left(x + 60\right) \cdot \cos\left( 68.52 \right)\) for the variable \(x\).

MathBot Answer:

The solution is: \[x = \frac{51 \left(-352961 + 964000 \cos{\left(\frac{1713}{25} \right)}\right)}{200 \cdot \left(1500 - 4097 \cos{\left(\frac{1713}{25} \right)}\right)} \approx -59.997329\]

\[\begin{aligned}{x}^{2} + {152.5}^{2} &= {163.88}^{2} + {\left( x + 60 \right)}^{2} - 2 \cdot 163.88 \left(x + 60\right) \cdot \cos\left( 68.52 \right)\\x^{2} + 23256.25 &= x^{2} + x \left(120 - \frac{8194 \cos{\left(68.52 \right)}}{25}\right) + \left(30456.6544 - \frac{98328 \cos{\left(68.52 \right)}}{5}\right)\\x \left(-120 + \frac{8194 \cos{\left(68.52 \right)}}{25}\right) &= 7200.4044 - \frac{98328 \cos{\left(68.52 \right)}}{5}\\x &= \frac{7200.4044 - \frac{98328 \cos{\left(68.52 \right)}}{5}}{-120 + \frac{8194 \cos{\left(68.52 \right)}}{25}}\end{aligned}\]

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