Question

find the length of side b.
c = 61.3° b = 48.7° b = ?
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we can use $\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}$. We know side $AB = 14$, angle $A=70^{\circ}$, and we want to find side $b = AC$.
So, $\frac{b}{\sin B}=\frac{AB}{\sin C}$.

Step2: Substitute the known values

Substitute $AB = 14$, $B = 48.7^{\circ}$, and $C = 61.3^{\circ}$ into the formula:
$b=\frac{14\times\sin48.7^{\circ}}{\sin61.3^{\circ}}$.
We know that $\sin48.7^{\circ}\approx0.752$ and $\sin61.3^{\circ}\approx0.877$.
Then $b=\frac{14\times0.752}{0.877}$.

Step3: Calculate the value of $b$

First, calculate $14\times0.752 = 10.528$.
Then, $b=\frac{10.528}{0.877}\approx12.0$.

Answer:

$12.0$