Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{6}$ $pi / 6$ . If one side of the triangle has a length of 8, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-02-15T10:47:30

Longest possible Perimeter of the triangle

$P = a + b + c = 38.9096$ $P = a + b + c = color(green)(38.9096$

Third angle measures $π - (\frac{5 π}{12}) - (\frac{π}{6}) = (\frac{5 π}{12})$ $pi - ((5pi)/12) - (pi/6) = ((5pi)/12)$

It’s an isosceles triangle.

To get the longest perimeter, length 8 should correspond to the least anle $\frac{π}{6}$ $pi/6$

$:. a / sin ((5pi)/12)= b / sin ((5pi)/12) = 8 / sin (pi/6)$

$a = b = (8 * sin ((5pi)/12)) / sin (pi/6) = 16 * sin ((5pi)/12) = 15.4548$

Longest possible Perimeter of the triangle $P = a + b + c = 15.4548 + 15.4548 + 8 = color(green)(38.9096$

Two corners of a triangle have angles of (5 pi )/ 12 5π12 (5 pi )/ 12 and pi / 6 π6 pi / 6 . If one side of the triangle has a length of 8, what is the longest possible perimeter of the triangle?