Question

question 10 (mandatory) (1 point) in △abc, a = 6.9 m, b = 15.7 m, and ∠c = 39°. determine c to the nearest tenth of a metre. a) 9.9 m b) 7.3 m c) 14.5 m d) 11.2 m

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Given \(a = 6.9\), \(b=15.7\), and \(C = 39^{\circ}\), substitute these values into the formula.

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Step2: Solve for \(c\)

Take the square root of \(c^{2}\). \(c=\sqrt{123.63}\approx11.1\) (rounded to the nearest tenth).

Answer:

d) \(11.2\) m (Note: There might be a slight difference in rounding during intermediate steps. If we use more precise values for \(\cos(39^{\circ})\approx0.7771459615\)

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