Question

find the length of side c.
law of cosines: $c^2 = a^2 + b^2 - 2ab \cdot \cos(c)$
round your answer to the nearest hundredth.
(image of triangle with labels: c with angle 73°, side a=8, side b=14, side c=? at angle a)

Explanation:

Step1: Identify given values

We have \(a = 8\), \(b = 14\), and \(\angle C=73^\circ\). The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cdot\cos(C)\).

Step2: Substitute values into the formula

Substitute \(a = 8\), \(b = 14\), and \(\cos(73^\circ)\approx0.2924\) into the formula:

$$
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$$

Step3: Calculate each term

First, calculate \(224\times0.2924 = 224\times0.2924 = 65.4976\). Then, \(260-65.4976 = 194.5024\).

Step4: Find \(c\)

Take the square root of \(194.5024\): \(c=\sqrt{194.5024}\approx13.95\) (rounded to the nearest hundredth).

Answer:

\(13.95\)