Question

quiz 8: solve right, scalene, and obtuse t
6 points possible answered: 1/6
question 2
find the length of side x. round to the nearest tenth.
(image of a triangle with sides 7, x and angles 40°, 110°)
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, if we assume the side of length \(7\) is opposite the \(30^{\circ}\) angle and side \(x\) is opposite the \(110^{\circ}\) angle. So \(\frac{7}{\sin 30^{\circ}}=\frac{x}{\sin 110^{\circ}}\).
Since \(\sin 30^{\circ}=\frac{1}{2}\), the equation becomes \(x = 7\times\frac{\sin 110^{\circ}}{\sin 30^{\circ}}\).
We know that \(\sin 110^{\circ}=\sin(90^{\circ} + 20^{\circ})=\cos 20^{\circ}\approx0.94\).
Substituting the values: \(x = 7\times\frac{0.94}{0.5}=7\times1.88 = 13.2\).

Answer:

\(13.2\)