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 = 36°, b = 30°, a = 9
a =
°
b =
°
c =
°
a =
b =
c =
question help: video ebook
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Explanation:

Step1: Find angle \(C\)

Sum of angles in a triangle is \(180^{\circ}\). So \(C = 180^{\circ}-A - B\).
Substitute \(A = 36^{\circ}\) and \(B=30^{\circ}\), then \(C=180^{\circ}-36^{\circ}-30^{\circ}=114^{\circ}\).

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

The Law of Sines is \(\frac{a}{\sin A}=\frac{b}{\sin B}\).
We know \(a = 9\), \(A = 36^{\circ}\), \(B = 30^{\circ}\).
So \(b=\frac{a\sin B}{\sin A}\).
\(\sin36^{\circ}\approx0.5878\), \(\sin30^{\circ}=0.5\).
\(b=\frac{9\times0.5}{0.5878}=\frac{4.5}{0.5878}\approx7.66\).

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

By the Law of Sines \(\frac{a}{\sin A}=\frac{c}{\sin C}\).
\(\sin114^{\circ}\approx0.9135\).
\(c=\frac{a\sin C}{\sin A}=\frac{9\times0.9135}{0.5878}=\frac{8.2215}{0.5878}\approx13.99\).

Answer:

\(A = 36.00^{\circ}\)
\(B = 30.00^{\circ}\)
\(C = 114.00^{\circ}\)
\(a = 9.00\)
\(b\approx7.66\)
\(c\approx13.99\)