Digital ACT Math Practice Question #1163
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Use the Law of Cosines: c^2 = a^2 + b^2 - 2ab\cos(C). Remember that cos(120°) = -1/2, making the last term positive.
Desmos Shortcut: Type sqrt(7^2 + 10^2 - 2*7*10*cos(120 deg)) into Desmos. It gives ~14.7986. Check sqrt(219) = 14.7986.
Apply the Law of Cosines: \( PR^2 = PQ^2 + QR^2 - 2(PQ)(QR)\cos(120^\circ) \). Since \( \cos(120^\circ) = - rac{1}{2} \), substitute the known values: \[ PR^2 = 7^2 + 10^2 - 2(7)(10)\left(- rac{1}{2} ight) \] \[ PR^2 = 49 + 100 + 70 = 219 \...
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