Question

find g.
write your answer as an integer or as a decimal rounded to the n

Explanation:

Step1: Find angle at H

The sum of angles in a triangle is \(180^\circ\). So, \(\angle H = 180^\circ - 55^\circ - 98^\circ = 27^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{g}{\sin G}=\frac{FG}{\sin H}\). We know \(FG = 5\), \(\angle G = 98^\circ\), \(\angle H = 27^\circ\). So, \(\frac{g}{\sin 98^\circ}=\frac{5}{\sin 27^\circ}\).

Step3: Solve for g

First, calculate \(\sin 98^\circ\approx0.9903\) and \(\sin 27^\circ\approx0.4540\). Then, \(g=\frac{5\times\sin 98^\circ}{\sin 27^\circ}=\frac{5\times0.9903}{0.4540}\approx\frac{4.9515}{0.4540}\approx10.9\) (rounded to one decimal place).

Answer:

\(10.9\)