Question

quiz 8: solve right, scalene, and obtuse triangles
6 points possible answered: 2/6
question 3
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 two decimal places, if necessary.
a = 21°, b = 19°, a = 5
a =
°
b =
°
c =
°
a =
b =
c =
question help: video ebook
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Explanation:

Step1: Find angle \(C\)

The sum of angles in a triangle is \(180^{\circ}\). So \(C = 180^{\circ}-A - B\).
Substitute \(A = 21^{\circ}\) and \(B=19^{\circ}\):
\(C=180^{\circ}-21^{\circ}-19^{\circ}=140^{\circ}\)

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

The Law of Sines is \(\frac{a}{\sin A}=\frac{b}{\sin B}\).
We know \(a = 5\), \(A = 21^{\circ}\), \(B = 19^{\circ}\).
So \(b=\frac{a\sin B}{\sin A}\)
\(\sin21^{\circ}\approx0.3584\), \(\sin19^{\circ}\approx0.3256\)
\(b=\frac{5\times0.3256}{0.3584}\approx4.54\)

Step3: Use the Law of Sines to find \(c\)

By the Law of Sines \(\frac{a}{\sin A}=\frac{c}{\sin C}\)
\(\sin C=\sin140^{\circ}\approx0.6428\)
\(c=\frac{a\sin C}{\sin A}=\frac{5\times0.6428}{0.3584}\approx8.98\)

Answer:

\(A = 21.00^{\circ}\)
\(B = 19.00^{\circ}\)
\(C = 140.00^{\circ}\)
\(a = 5.00\)
\(b\approx4.54\)
\(c\approx8.98\)