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 of longest side of the triangle is:
Answers
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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