# SOLUTION: Two angles of a triangle measure 75° and 51°. The side opposite the largest angle measures 25 inches. How long is the shortest side?

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 Click here to see ALL problems on Geometry Word Problems 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(2733)   (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.