Question

quiz 8: solve right, scalene, and obtuse triangles
6 points possible answered: 4/6
question 5
solve for the remaining sides and angles if possible (if not, answer \dne\ in all answer boxes). as in the text, (a, a), (b, b), and (c, c) are angle - side opposite pairs. round to one decimal places, if necessary.
a = 104°, b = 27, c = 33
a =
°
b =
°
c =
°
a =
b =
c =
question help: video ebook
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Explanation:

Step1: Use the Law of Cosines to find side \(a\)

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\).
Substitute \(A = 104^{\circ}\), \(b = 27\), and \(c = 33\) into the formula:

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Step2: Use the Law of Sines to find angle \(B\)

The Law of Sines formula is \(\frac{\sin B}{b}=\frac{\sin A}{a}\).
Substitute \(A = 104^{\circ}\), \(a\approx47.4\), and \(b = 27\) into the formula:

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\(B=\sin^{-1}(0.553)\approx33.6^{\circ}\)

Step3: Use the angle - sum property of a triangle to find angle \(C\)

Since \(A + B + C=180^{\circ}\), then \(C = 180^{\circ}-A - B\).
Substitute \(A = 104^{\circ}\) and \(B\approx33.6^{\circ}\) into the formula:
\(C=180^{\circ}-104^{\circ}-33.6^{\circ}=42.4^{\circ}\)

Answer:

\(A = 104^{\circ}\), \(B\approx33.6^{\circ}\), \(C\approx42.4^{\circ}\), \(a\approx47.4\), \(b = 27\), \(c = 33\)