Question

quiz 8: solve right, scalene, and obtuse triangles
6 points possible answered: 1/6
question 2
find the length of side ( x ). round to the nearest tenth.
triangle with side 20, angles 40° and 110°, side ( x )
( x = )
question help: video ebook

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Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(A\). Then \(A = 180^{\circ}-40^{\circ}-110^{\circ}=30^{\circ}\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here, let \(a = x\), \(A = 110^{\circ}\), \(b = 20\), \(B = 30^{\circ}\). So \(\frac{x}{\sin110^{\circ}}=\frac{20}{\sin30^{\circ}}\).
Since \(\sin30^{\circ}=\frac{1}{2}\) and \(\sin110^{\circ}\approx0.9397\), we can rewrite the equation as \(x=\frac{20\times\sin110^{\circ}}{\sin30^{\circ}}\).
Substitute the values: \(x=\frac{20\times0.9397}{0.5}\).
Calculate \(20\times0.9397 = 18.794\), then \(x=\frac{18.794}{0.5}=37.588\approx37.6\).

Answer:

\(37.6\)