Final answer:
In triangle FGH, given angles F and G are 60 and 68 degrees respectively, angle H can be calculated as 52 degrees. Being the smallest angle, the side opposite to it, which is FG, is the shortest side of the triangle.
Step-by-step explanation:
The question involves determining which side of the triangle FGH is the shortest. In any triangle, the length of the sides is directly related to the angles opposite them. The larger the angle, the longer the opposite side; conversely, the smaller the angle, the shorter the opposite side.
In triangle FGH, we are given that m∠F = 60 degrees and m∠G = 68 degrees. The sum of angles in any triangle is 180 degrees, hence we can find the measure of angle H by subtracting the measures of angles F and G from 180 degrees:
m∠H = 180 - (m∠F + m∠G) = 180 - (60 + 68) = 180 - 128 = 52 degrees.
Since angle H is the smallest angle (52 degrees), the side opposite to it, which is side FG, is the shortest side of the triangle.