Question

consider a triangle abc like the one below. suppose that a=37, b=35, and c=3. (the figure is not drawn to scale.) solve the triangle. carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. if there is more than one solution, use the button labeled \or\. a = □°, b = □°, c = □°

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\), \(b^{2}=a^{2}+c^{2}-2ac\cos B\), \(c^{2}=a^{2}+b^{2}-2ab\cos C\). First, use \(a = 37\), \(b = 35\), \(c = 3\) in \(a^{2}=b^{2}+c^{2}-2bc\cos A\)

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\(A=\cos^{-1}(-0.6429)\approx130.0^{\circ}\)

Step2: Use the Law of Sines

The Law of Sines formula is \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). From \(\frac{a}{\sin A}=\frac{b}{\sin B}\), we have \(\sin B=\frac{b\sin A}{a}\)

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\(B=\sin^{-1}(0.7246)\approx46.5^{\circ}\)

Step3: Find angle \(C\)

Since \(A + B+C=180^{\circ}\), then \(C = 180^{\circ}-A - B\)

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Answer:

\(A = 130.0^{\circ}\), \(B = 46.5^{\circ}\), \(C = 3.5^{\circ}\)