Answer:
9.7 feet
Step-by-step explanation:
You can use the Law of Sines to solve this problem. The law states:
[tex]\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}[/tex]
Since the given triangle is ASA (angle-side-angle) and we can use the triangle angle sum theorem to find the third angle (sum of triangle angles is 180 degrees). We can therefore determine that angle G is 72 degrees because 180-90-18 is 72.
According to the diagram, we can input our values into the Law of Sines in order solve for FG. Now we can solve the ratio for FG.
[tex]\frac{sin72}{9.2} = \frac{sin90}{FG}[/tex]
sin90 is 1, so FG is equal to:
[tex]FG = \frac{9.2}{sin72}[/tex]
FG is equal to 9.67 feet, which is 9.7 when rounded to the nearest tenth of a foot.
