Question

1. the length of bc, to the nearest tenth of a cm, is

(record your answer in the numerical response box from left to right.)
in triangle abc, angle bac = 60°,
ab = 6 cm, and ac = 8 cm.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(BC^{2}=AB^{2}+AC^{2}-2(AB)(AC)\cos\angle BAC\). Given \(AB = 6\mathrm{cm}\), \(AC = 8\mathrm{cm}\), and \(\angle BAC=60^{\circ}\), substitute these values into the formula.

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Step2: Calculate \(BC^{2}\) and then \(BC\)

First, calculate \(36 + 64-48=52\). Then, find \(BC=\sqrt{52}\approx7.2\mathrm{cm}\) (since \(\sqrt{52}\approx7.211\) and we round to the nearest tenth).

Answer:

\(7.2\)