Question

find the measure of \\( \angle a \\). round to the nearest tenth of a degree.
\\( a = \\) question help: \\( \square \\) message instructor

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 110\), \(b = 120\), \(c = 135\), and \(C=\angle A\). Then \(135^{2}=110^{2}+120^{2}-2\times110\times120\times\cos A\).

Step2: Simplify the equation

First, calculate the squares: \(18225 = 12100+14400 - 26400\cos A\). Then \(18225=26500 - 26400\cos A\).

Step3: Solve for \(\cos A\)

Rearrange the equation: \(26400\cos A=26500 - 18225\). So \(26400\cos A = 8275\). Then \(\cos A=\frac{8275}{26400}\approx0.313447\).

Step4: Find the angle \(A\)

Take the inverse - cosine: \(A=\cos^{-1}(0.313447)\). Using a calculator, \(A\approx71.7^{\circ}\).

Answer:

\(71.7\)