A triangle has two corners with angles of # pi / 12 # and # pi / 2 #. If one side of the triangle has a length of #6 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-01-24T10:26:25

Largest possible area of the triangle is #color(green)(67.1769)#

Three angles are #beta = pi/12, gamma = /_C = pi/2, alpha = (5pi)/12#

It’s a right triangle.and length 6 should be opposite to the vertex having smallest angle #pi/12#
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Area of the largest possible triangle

#A_t =(1/2) * b * a = (1/2) * b *( b / tan beta)#

#A_t = (1/2) * 6 * (6/tan (pi/12)) ~~ color (green)(67.1769)#