Answer: In triangle AGH, we can use the Law of Sines. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
so, a/sin(A) = b/sin(B) = c/sin(C) = 2R where R is the circumradius of the triangle.
Given, g = 9.6 inches, m/I = 80° and m/G = 15°
AG = h, angle A = (180 - 80) = 100, angle G = (180-15) = 165
So we can use the Law of Sines to find the h,
h/sin(100) = g/sin(165) = 9.6 / sin(165) = 9.6 / sin(165) = 9.6 / 0.9659 = 9.98 inch.
Rounded to the nearest 10th of an inch, h = 9.98 inches.
Explanation: