Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ 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 $\frac{5 π}{8}$ $(5 pi )/ 8$ 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 · 2018-05-03T12:08:38

$Longest possible perimeter P = 53.45 sq units$ $color(brown)("Longest possible perimeter " P = 53.45 " sq units"$

Explanation:

$ˆ A = \frac{5 π}{8}, ˆ B = \frac{π}{12}, ˆ C = π - \frac{5 π}{8} - \frac{π}{12} = \frac{7 π}{24}$ $hat A = (5pi)/8, hat B = pi/12, hat C = pi - (5pi)/8 - pi/12 = (7pi)/24$

$color(blue)("As per Law of Sines,' color(crimson)(a / sin A = b / sin B = c / sin C$

To get the longest perimeter, side of length 7 should correspond to least angle $hat B = pi/12$

$:. a / sin ((5pi)/8) = 7 / sin (pi/12) = c / sin ((7pi)/24)$

$a = (7 * sin ((5pi)/8)) / sin (pi/12) ~~ 24.99$

$c = (7 sin ((7pi)/24)) / sin (pi/12) ~~ 21.46$

$color(brown)("Longest possible perimeter " P = 7 + 24.99 + 21.46 = 53.45$

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ 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 (5 pi )/ 8 5π8 (5 pi )/ 8 and ( pi ) / 12 π12 ( pi ) / 12 . If one side of the triangle has a length of 7 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 $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?