math 2201 september 2025 d)solve for θ

Question

Accepted Answer

# Explanation:
## Step1: Apply the Law of Cosines
The Law of Cosines formula for finding an angle $\theta$ in a triangle with sides $a = 40.4$, $b = 46.5$, $c = 52.1$ is $\cos\theta=\frac{a^{2}+b^{2}-c^{2}}{2ab}$.
Substitute the values:
$$
\begin{align*}
a^{2}&=(40.4)^{2}=1632.16\
b^{2}&=(46.5)^{2}=2162.25\
c^{2}&=(52.1)^{2}=2714.41\
2ab&=2\times40.4\times46.5 = 3777.6
\end{align*}
$$
$$
\begin{align*}
a^{2}+b^{2}-c^{2}&=1632.16 + 2162.25- 2714.41\
&=3794.41 - 2714.41\
&=1080
\end{align*}
$$
So, $\cos\theta=\frac{1080}{3777.6}\approx0.286$.
## Step2: Find the angle $\theta$
$\theta=\cos^{- 1}(0.286)$
Using a calculator, $\theta\approx73.4^{\circ}$

# Answer:
$\theta\approx73.4^{\circ}$

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Question

Explanation:

Step1: Apply the Law of Cosines

Step2: Find the angle $\theta$

Answer: