The measures of two angles of a triangle are and 36° and 75° . The length of the shortest side of a triangle is 10cm . The length

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1. Given : The measures of two angles of a triangle are 36° and 75°

   The length of the shortest side of a triangle is 10cm

   To Find : The length of longest side of the triangle

   Solution:

   The measures of two angles of a triangle are 36° and 75°

   Sum of three angles of triangle = 180°

   Hence third angle = 180° – (36° + 75°) = 69°

   Largest angle = 75°

   Smallest angle = 36°

   Side opposite to smallest angle is smallest

   and side opposite to largest angle is largest

   Using Sine rule

   a/SinA = b/SinB = c/SinC

   10 / Sin36° = Largest side / Sin 75°

   => Largest side = 10 * Sin 75° / Sin36°

   => Largest side = 10 * 1.643

   => Largest side = 16.43 cm

   longest side of the triangle is 16.43 cm

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