Digital ACT Math Practice Question #853
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When given two sides and the included angle, apply the Law of Cosines: \( c^2 = a^2 + b^2 - 2ab\cos(C) \).
TI-84 / Calculator Shortcut: Compute \( 7^2 + 8^2 - 2 \times 7 \times 8 \times 0.25 = 85 \). The answer is simply \( \sqrt{85} \).
Use the Law of Cosines: \( b^2 = a^2 + c^2 - 2ac\cos(C) \). Here, \( a = BC = 8 \), \( c = AB = 7 \), and \( \cos(C) = \frac{1}{4} \): \[ AC^2 = 8^2 + 7^2 - 2(8)(7)\left(\frac{1}{4}\right) \] \[ AC^2 = 64 + 49 - 112\left(\frac{1}{4}\right) ...
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