Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $16$ $16$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $16$ $16$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-02-27T16:24:21

Longest possible perimeter

$P = a + b + c = 137.532$ $P = a + b + c = color (blue)(137.532)$ units

Explanation:

$A = \frac{5 π}{13}, B = \frac{π}{12}, C = π - \frac{π}{12} - \frac{5 π}{12} = \frac{π}{2}$ $A = (5pi)/13, B = pi / 12, C = pi - pi/12 - (5pi)/12 = pi/2$

To get the longest perimeter, length 16 should correspond to $ˆ B = (\frac{π}{12})$ $hat B= (pi/12)$

Applying law of sines,

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$a = \frac{b \cdot sin A}{sin B} = \frac{16 \cdot sin (\frac{5 π}{12})}{sin (\frac{π}{12})} = 59.7128$ $a = (b * sin A) / sin B = (16 * sin ((5pi)/12)) / sin (pi/12) = 59.7128$

$c = \sqrt{a^{2} + b^{2}} = \sqrt{16^{2} + {59.7128}^{2}} = 61.8192$ $c = sqrt(a^2 + b^2) = sqrt(16^2 + 59.7128^2) = 61.8192$

Longest possible perimeter

$P = a + b + c = 16 + 59.7128 + 61.8192 = 137.532$ $P = a + b + c = 16 + 59.7128 + 61.8192 = color (blue)(137.532)$

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $16$ $16$ , 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 )/ 12 5π12 (5 pi )/ 12 and ( pi ) / 12 π12 ( pi ) / 12 . If one side of the triangle has a length of 16 16 16 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $16$ $16$ , what is the longest possible perimeter of the triangle?