Question

solve for angle c. evaluate and simplify, using cos-1. 9^2 = 4^2 + 7^2 - 2(4)(7)cosc c = ?° enter the measure of angle c in degrees. round to the nearest tenth.

Explanation:

Step1: Simplify the equation

First, calculate the squares: $9^{2}=81$, $4^{2} = 16$, $7^{2}=49$.
The equation $9^{2}=4^{2}+7^{2}-2(4)(7)\cos C$ becomes $81 = 16 + 49-56\cos C$.

Step2: Combine like - terms

$16 + 49=65$, so the equation is $81=65 - 56\cos C$.
Subtract 65 from both sides: $81 - 65=-56\cos C$, which simplifies to $16=-56\cos C$.

Step3: Solve for $\cos C$

Divide both sides by - 56: $\cos C=\frac{16}{-56}=-\frac{2}{7}$.

Step4: Find the angle C

$C=\cos^{-1}(-\frac{2}{7})$. Using a calculator, $C\approx 106.6^{\circ}$ (rounded to the nearest tenth).

Answer:

$106.6$