Question

quiz 8: solve right, scalene, and obtuse triangles
6 points possible answered: 3/6
question 4
find the length of side x. round to the nearest tenth.
triangle with sides 22.1, 17, angle 72° between them, side x opposite?
x =
question help: video ebook
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Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(x^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 22.1\), \(b = 17\), and \(C=72^{\circ}\).
So, \(x^{2}=22.1^{2}+17^{2}-2\times22.1\times17\times\cos(72^{\circ})\).
First, calculate \(22.1^{2}=488.41\), \(17^{2} = 289\), and \(\cos(72^{\circ})\approx0.3090\).
Then, \(2\times22.1\times17\times0.3090=2\times22.1\times17\times0.3090 = 229.986\).
Now, \(x^{2}=488.41 + 289-229.986\).

Step2: Simplify the expression

\(x^{2}=488.41+289 - 229.986=547.424\).

Step3: Find \(x\)

Take the square root of \(x^{2}\), \(x=\sqrt{547.424}\approx23.4\).

Answer:

\(23.4\)