Question

question 16 (mandatory) (1 point)
in △abc, a = 5.4 m, b = 7.2 m, and c = 10.0 m. determine ∠c to the nearest degree.
a) 92°
b) 97°
c) 104°
d) 108°

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Rearranging for \(\cos C\), we get \(\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}\).
Substitute \(a = 5.4\), \(b = 7.2\), and \(c = 10.0\) into the formula:

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Step2: Find the angle \(C\)

Since \(C=\cos^{-1}(-0.2444)\), using a calculator, \(C\approx104^{\circ}\)

Answer:

C. \(104^{\circ}\)