In ΔFGH, FH = 7ft, FG = 12ft, and m∠F = 70°. Find m∠G. Round your answer to nearest tenth.
To find the measure of ∠G, we will use the Law of Cosines.
c^2 = a^2 + b^2 - 2ab cos(C), where c is the side opposite to angle C.
Let side FH be 'a', side FG be 'b', and angle F be 'C'.
Therefore,
c^2 = 7^2 + 12^2 - 2(7)(12)cos(70°)
c^2 = 49 + 144 - 168cos(70°)
c^2 = 193.076
c ≈ 13.9
Now, using the Law of Sines, we can find the measure of angle G.
sin(G)/12 = sin(70)/13.9
sin(G) = (12/13.9)sin(70)
sin(G) ≈ 0.879
G ≈ sin^-1(0.879)
G ≈ 62.4°
Therefore, m∠G ≈ 62.4°.