Find the requested information using the law of cosines and/or the law of sines. Round to three decimal places.
-A triangle has side $\mathrm { c } = 4$ and angles $\mathrm { A } = \frac { \pi } { 3 }$ and $\mathrm { B } = \frac { \pi } { 4 }$. Find the length $\mathrm { b }$ of the side opposite $\mathrm { B }$.
A) $0.732$
B) $2.928$
C) $3.586$
D) $0.183$

Question

Quizplus · Accepted Answer

To find the length $b$, we can use the Law of Sines: $\frac{b}{\sin B} = \frac{c}{\sin C}$. First, find angle $C$ by subtracting angles $A$ and $B$ from $\pi$: $C = \pi - \frac{\pi}{3} - \frac{\pi}{4} = \frac{5\pi}{12}$. Then, use the Law of Sines: $b = c \cdot \frac{\sin B}{\sin C} = 4 \cdot \frac{\sin(\pi/4)}{\sin(5\pi/12)}$, which gives $b \approx 2.928$.

Find the Requested Information Using the Law of Cosines And/or c=4\mathrm { c } = 4c=4

Find the Requested Information Using the Law of Cosines And/or $\mathrm { c } = 4$