Two corners of a triangle have angles of (3 pi ) / 4 and pi / 6 . If one side of the triangle has a length of 9 , what is the longest possible perimeter of the triangle?
1 Answer
Longest Possible perimeter is
Explanation:
With the given two angles we can find the 3rd angle by using the concept that sum of all three angles in a triangle is
Hence, the third angle is
Now, let's say
Using Sine Rule we have,
where, a, b and c are the length of the sides opposite to
Using above set of equations, we have the following:
Now, to find the longest possible perimeter of the triangle
Assuming,
Assuming,
Assuming,
Therefore, Longest possible perimeter of the given triangle is