Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . 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 $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . 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 · 2018-06-02T12:53:19

Perimeter $P = a + b + c = 36.83$ $color(blue)( P = a + b + c = 36.83$

Explanation:

$ˆ A = \frac{5 π}{8}, ˆ B = \frac{π}{4}, ˆ C = π - \frac{5 π}{8} - \frac{π}{4} = \frac{π}{8}$ $hat A = (5pi)/8, hat B = pi/4, hat C = pi - (5pi)/8 - pi/4 = pi/8$

Least angle $ˆ C = \frac{π}{8}$ $hat C = pi/8$ should correspond to the side 7 to get the longest perimeter.

Applying Law of Sines,

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

$a = \frac{c sin A}{sin C} = \frac{7 \cdot sin (\frac{5 π}{8})}{sin (\frac{π}{8})} = 16.9$ $a = (c sin A) / sin C = (7 * sin((5pi)/8)) / sin (pi/8) = 16.9$

$b = \frac{7 \cdot sin (\frac{π}{4})}{sin (\frac{π}{8})} = 12.93$ $b = (7 * sin (pi/4)) / sin (pi/8) = 12.93$

Perimeter $P = a + b + c = 16.9 + 12.93 + 7 = 36.83$ $color(blue)( P = a + b + c = 16.9 + 12.93 + 7 = 36.83$

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . 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 5π8 (5 pi )/ 8 and π4 ( pi ) / 4 . 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 $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?