In ∆FGH, FH = 8ft FG = 13H and m angle F = 72' , Find the length of HG. Label the diagram to help you. Round your answer to the nearest whole number
Hg=?
Answer 13 ft
To solve for HG, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where c is the side opposite to the angle we know (angle F), a = FG, b = FH, and C = angle F.
Plugging in the values we know:
HG^2 = 13^2 + 8^2 - 2(13)(8)*cos(72)
Simplifying:
HG^2 = 169 + 64 - 208*cos(72)
HG^2 = 233.63
HG ≈ 15.29 ft
Rounded to the nearest whole number, HG ≈ 15 ft.
Therefore, the length of HG is approximately 15 feet.