A piece of conduit 39.0 ft long cuts across the corner of a room, as shown in the illustration. Find length x and angle A. Round each answer to the appropriate number of significant digits.
A) $\angle A =$ 59.7°, x = 34.7 ft
B) $\angle A =$ 61.4°, x = 33.0 ft
C) $\angle A =$ 60.8°, x = 34.1 ft
D) $\angle A =$ 58.6°, x = 31.9 ft
E) $\angle A =$ 59.1°, x = 32.4 ft

Question

A piece of conduit 39.0 ft long cuts across the corner of a room, as shown in the illustration. Find length x and angle A. Round each answer to the appropriate number of significant digits. 
A) $\angle A =$ 59.7°, x = 34.7 ft 
B) $\angle A =$ 61.4°, x = 33.0 ft 
C) $\angle A =$ 60.8°, x = 34.1 ft 
D) $\angle A =$ 58.6°, x = 31.9 ft 
E) $\angle A =$ 59.1°, x = 32.4 ft

Quizplus · Accepted Answer

Using the Pythagorean theorem, we can find the length of the diagonal of the room:
\begin{align*}
c^2 &= 12^2 + 16^2 + 8^2 \
c &= 20
\end{align*}
Next, we can use the law of cosines to find the angle $\angle A$:
\begin{align*}
c^2 &= a^2 + b^2 - 2ab\cos A \
20^2 &= 12^2 + 16^2 - 2(12)(16)\cos A \
\cos A &= \frac{175}{384} \
\angle A &\approx 60.8^\circ
\end{align*}
Finally, we can use the law of sines to find $x$:
\begin{align*}
\frac{x}{\sin A} &= \frac{c}{\sin(\pi/2)} \
x &= c\sin A \
x &\approx 34.1	ext{ ft}
\end{align*} 
Therefore, the best choice is C.

A Piece of Conduit 39 ∠A=\angle A =∠A= 597°, X = 34

A Piece of Conduit 39 $\angle A =$ 597°, X = 34