Question

use the law of sines. find b to the nearest tenth.

Explanation:

Step1: Find angle \( C \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( C=180^{\circ}-44^{\circ}-48^{\circ}=88^{\circ} \).

Step2: 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 have \( \frac{b}{\sin B}=\frac{BC}{\sin A} \). Substituting the values: \( B = 44^{\circ}\), \( BC = 51\), \( A=48^{\circ}\). So, \( b=\frac{51\times\sin44^{\circ}}{\sin48^{\circ}} \).
We know that \( \sin44^{\circ}\approx0.6947\) and \( \sin48^{\circ}\approx0.7431 \). Then \( b=\frac{51\times0.6947}{0.7431}=\frac{35.4297}{0.7431}\approx47.7 \)

Answer:

\( 47.7 \)