Question

try it yourself. g. given a = 45°, a = x, b =?, b = 72.9, c =?, c = 89.5 home|work!! see google classroom!! if you need help, please reach out ©

Explanation:

Step1: Recall the Law of Cosines

The Law of Cosines formula for finding side \(a\) in a triangle with sides \(b\), \(c\) and included - angle \(A\) is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). Given \(b = 73.9\), \(c = 89.5\), and \(A = 45^{\circ}\), and \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\).

Step2: Calculate \(b^{2}\), \(c^{2}\) and \(2bc\cos A\)

\(b^{2}=(73.9)^{2}=5469.21\), \(c^{2}=(89.5)^{2}=8010.25\), and \(2bc\cos A = 2\times73.9\times89.5\times0.707=2\times73.9\times89.5\times\frac{\sqrt{2}}{2}\approx9353.58\).

Step3: Calculate \(a^{2}\)

\(a^{2}=b^{2}+c^{2}-2bc\cos A=5469.21 + 8010.25-9353.58=4125.88\).

Step4: Calculate \(a\)

\(a=\sqrt{4125.88}\approx64.2\).

Answer:

\(a\approx64.2\)