Question

find the measure of angle c. law of cosines: $c^{2}=a^{2}+b^{2}-2abcdot\cos c$ round your final answer to the nearest tenth.

Explanation:

Step1: Rearrange law of cosines

Given $c^{2}=a^{2}+b^{2}-2ab\cos C$, we can rewrite it for $\cos C$ as $\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}$.

Step2: Substitute values

Substitute $a = 8$, $b = 16$, and $c = 17$ into the formula:
$\cos C=\frac{8^{2}+16^{2}-17^{2}}{2\times8\times16}=\frac{64 + 256-289}{256}=\frac{320 - 289}{256}=\frac{31}{256}\approx0.121$.

Step3: Find angle C

$C=\cos^{-1}(0.121)$. Using a calculator, $C\approx83.0^{\circ}$.

Answer:

$83.0$