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

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

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

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