Two corners of a triangle have angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $pi / 12$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $pi / 12$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-05-20T06:39:41

Longest possible perimeter of the triangle is

$= 39.64$ $color(blue)(= 39.64$ units

Explanation:

$ˆ A = \frac{3 π}{4}, ˆ B = \frac{π}{12}, ˆ C = π - \frac{3 π}{4} - \frac{π}{12} = \frac{π}{6}$ $hat A = (3pi)/4, hat B = pi/12, hat C = pi - (3pi)/4 - pi/12 = pi/6$

To get the longest perimeter, side of length 7 should correspond to the least angle $\frac{π}{12}$ $pi/12$

Applying Law of Sines,

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b /sin B = c / sin C$

$\frac{a}{sin (\frac{3 π}{4})} = \frac{7}{sin (\frac{π}{12})} = \frac{c}{sin (\frac{π}{6})}$ $a/ sin ((3pi)/4) = 7 / sin (pi/12) = c / sin (pi/6)$

$a = \frac{7 \cdot sin (\frac{3 π}{4})}{sin (\frac{π}{12})} = 19.12$ $a = (7 * sin((3pi)/4))/sin(pi/12) =19.12$

$c = \frac{7 \cdot sin (\frac{π}{6})}{sin (\frac{π}{12})} = 13.52$ $c = (7*sin(pi/6))/sin(pi/12) = 13.52$

Perimeter $= a + b + c = 19.12 + 7 + 13.52 = 39.64$ $= a + b+ c = 19.12+ 7 + 13.52 = 39.64$

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Two corners of a triangle have angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $pi / 12$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of 3π4(3 pi ) / 4 and π12 pi / 12 . If one side of the triangle has a length of 77 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $pi / 12$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?