Question

8 Solve for C. 16 17 C= [?]° Measure of Angle C Round your final answer to the nearest tenth. Law of Cosines: c²= a'+ b² - 2ab•cosC Enter​

Answer 1

To solve for C, we would need to know the length of side c. Without that information, we cannot determine the value of angle C.

Explanation:

Using this assumption, we can rewrite the equation as:

c² = 16² + 17² - 2(16)(17)·cos(C)

c² = 256 + 289 - 544·cos(C)

c² = 545 - 544·cos(C)

Answer 2

C = 83.0°

Explanation:

This triangle has three sides, with lengths of 8 units, 16 units, and 17 units. The angle formed between the sides measuring 8 units and 16 units is angle C. Angle C is opposite the side measuring 17 units.

To find the measure of angle C, we can use the Law of Cosines.

`\boxed{\begin{array}{l}\underline{\textsf{Law of Cosines}}\\\\c^2=a^2+b^2-2ab \cos C\\\\\textsf{where $a, b$ and $c$ are the sides,}\\\textsf{and $C$ is the angle opposite side $c$.}\\\end{array}}`

In this case:

• a = 8
• b = 16
• c = 17
• C = C

Substitute the values of a, b, and c into the formula, and solve for C:

`\begin{aligned}c^2&=a^2+b^2-2ab\cos C\\\\17^2&=8^2+16^2-2(8)(16)\cos C\\\\289&=64+256-256\cos C\\\\289&=320-256\cos C\\\\289-320&=320-256\cos C-320\\\\-31&=-256\cos C\\\\(-31)/(-256)&=(-256\cos C)/(-256)\\\\(31)/(256)&=\cos C\\\\\cos C&=(31)/(256)\\\\C&=\cos^(-1)\left((31)/(256)\right)\\\\C&=83.04476981...^(\circ)\\\\C&=83.0^(\circ)\; \sf (nearest\;tenth)\end{aligned}`

Therefore, the measure of angle C, rounded to the nearest tenth, is:

`\Large\boxed{\boxed{C=83.0^(\circ)}}`