a homeowner makes a corner closet for his tools in an inside corner of his workshop. the lengths of the sides of the corner closet are 34 inches, 35 inches, and 36 inches. what are the respective angles, in degrees? round to the nearest hundredth.

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Accepted Answer

# Explanation:
## Step1: Use the Law of Cosines
The Law of Cosines formula is $ \cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}$, $ \cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac}$, $ \cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}$. Let $a = 34$, $b = 35$, $c = 36$.
## Step2: Calculate angle $A$
$$
\begin{align*}
\cos A&=\frac{35^{2}+36^{2}-34^{2}}{2\times35\times36}\
&=\frac{1225 + 1296- 1156}{2520}\
&=\frac{1365}{2520}\
A&=\cos^{-1}(\frac{1365}{2520})\approx57.33^{\circ}
\end{align*}
$$
## Step3: Calculate angle $B$
$$
\begin{align*}
\cos B&=\frac{34^{2}+36^{2}-35^{2}}{2\times34\times36}\
&=\frac{1156+1296 - 1225}{2448}\
&=\frac{1227}{2448}\
B&=\cos^{-1}(\frac{1227}{2448})\approx58.82^{\circ}
\end{align*}
$$
## Step4: Calculate angle $C$
Since the sum of angles in a triangle is $180^{\circ}$, $C=180-(A + B)$
$$
\begin{align*}
C&=180-(57.33 + 58.82)\
&=63.85^{\circ}
\end{align*}
$$

# Answer:
The angles are approximately $57.33^{\circ}$, $58.82^{\circ}$, and $63.85^{\circ}$

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Question

Explanation:

Step1: Use the Law of Cosines

Step2: Calculate angle \(A\)

Step3: Calculate angle \(B\)

Step4: Calculate angle \(C\)

Answer: