Question 322449: Two angles of a triangle measure 75° and 51°. The side opposite the largest angle measures 25 inches. How long is the shortest side? Answer by nyc_function(2741) (Show Source):
You can put this solution on YOUR website! I know that this is a geometry question but it can be solved using trigonometry.
We use the law of sines.
The sum of the angles of a triangle is 180 degrees.
To find the missing angle, add 51 + 75 and then subtract the sum from 180.
This will give you 54 degrees.
We now use the law of sines.
Let x = the missing side we want to find
sin51/x = sin75/25
x(sin75) = sin51(25)
x(sin75) = 19.42864904
x = 19.42864904/sin75
x = 20.11401756
The side opposite the smallest angle is 20 inches.
