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question 2
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how long, to the nearest feet and inches, is the right rafter in the roof shown?
select one:
a. 346\
b. 336\
c. 330\
d. 340\

Explanation:

Step1: Convert angle - measure to decimal degrees

First, convert $43'6''$ to decimal degrees. Since $1'=\frac{1}{60}$ degrees and $1''=\frac{1}{3600}$ degrees.
$43'6'' = 43+\frac{6}{60}=43.1$ feet.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ in a triangle. Let the side of length $43.1$ feet be $a$, the right - rafter be $b$, the angle opposite to $a$ be $A = 180-(50 + 46)=84^{\circ}$, and the angle opposite to $b$ be $B = 50^{\circ}$.
We have $\frac{b}{\sin50^{\circ}}=\frac{43.1}{\sin84^{\circ}}$.

Step3: Solve for $b$

$b=\frac{43.1\times\sin50^{\circ}}{\sin84^{\circ}}$.
We know that $\sin50^{\circ}\approx0.766$ and $\sin84^{\circ}\approx0.994$.
$b=\frac{43.1\times0.766}{0.994}=\frac{33.0146}{0.994}\approx33.214$ feet.

Step4: Convert decimal feet to feet and inches

The whole - number part of $33.214$ is the number of feet, which is $33$ feet. The decimal part $0.214\times12\approx2.57$ inches, which is approximately $3$ inches. So, to the nearest half - inch, $b\approx33'6''$.

Answer:

B. $33'6''$