In triangle FGH, measure angle F=60 degrees, measure angle H=52 degrees. Which side of triangle FGH is the shortest?
G = 180 - 52 - 60 = 68
so H is smallest angle so the side opposite H is shortest
To determine which side of triangle FGH is the shortest, we need to use the concept of angles in a triangle. In a triangle, the sum of all angles is always 180 degrees.
Given that the measure of angle F is 60 degrees and the measure of angle H is 52 degrees, we can find the measure of angle G by subtracting the sum of angles F and H from 180 degrees.
Angle G = 180 degrees - (angle F + angle H)
Angle G = 180 degrees - (60 degrees + 52 degrees)
Angle G = 180 degrees - 112 degrees
Angle G = 68 degrees
Now, we can analyze the sides of the triangle. In a triangle, the side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.
Since angle G measures 68 degrees, it is the largest angle in triangle FGH. Therefore, the side opposite to angle G, which is side FG, is the longest side.
Conversely, since angle F measures 60 degrees, it is the smallest angle in triangle FGH. Therefore, the side opposite to angle F, which is side GH, is the shortest side.
To summarize, the shortest side in triangle FGH is side GH.