Question

find the length of side b.
round to the nearest tenth.

Explanation:

Step1: Find angle \( A \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( A=180^{\circ}-100^{\circ}-35^{\circ}=45^{\circ} \).

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{a}{\sin A}=\frac{b}{\sin B} \). We know \( a = 18.5 \), \( A = 45^{\circ} \), and \( B=100^{\circ} \). Then \( b=\frac{a\sin B}{\sin A} \).
Substitute the values: \( b=\frac{18.5\times\sin(100^{\circ})}{\sin(45^{\circ})} \).
Since \( \sin(100^{\circ})\approx0.9848 \) and \( \sin(45^{\circ})=\frac{\sqrt{2}}{2}\approx0.7071 \).
\( b=\frac{18.5\times0.9848}{0.7071}\).
\( b=\frac{18.2188}{0.7071}\approx25.8 \).

Answer:

\( 25.8 \)