Question

question 5 (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) 104° c) 97° 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 \(\cos C\) gives \(\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}\).
Substitute \(a = 5.4\), \(b = 7.2\), and \(c = 10.0\) into the formula:
\(\cos C=\frac{5.4^{2}+7.2^{2}-10.0^{2}}{2\times5.4\times7.2}\)
\(=\frac{29.16 + 51.84-100}{77.76}\)
\(=\frac{81 - 100}{77.76}\)
\(=\frac{-19}{77.76}\approx - 0.2443\)

Step2: Find the angle \(C\)

Since \(C=\cos^{-1}(\cos C)\), then \(C=\cos^{-1}(-0.2443)\)
Using a calculator, \(C\approx108^{\circ}\)

Answer:

d) \(108^{\circ}\)