Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of 9, 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 $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of 9, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-06-01T15:30:00

Longest possible perimeter $P = 33.21$ $color(crimson)(P = 33.21$

Explanation:

$ˆ A = \frac{5 π}{12}, ˆ B = \frac{π}{4}, ˆ C = \frac{π}{3}$ $hat A = (5pi)/12, hat B = pi/4, hat C = pi/3$

Least angle $\frac{π}{4}$ $pi/4$ should correspond to the side of length 9.

Applying Law of Sines,

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

$a = \frac{b sin A}{sin B} = \frac{9 \cdot sin (\frac{5 π}{12})}{sin (\frac{π}{4})} = 12.29$ $a = (b sin A) / sin B = (9 * sin ((5pi)/12)) / sin (pi/4) = 12.29$

$c = \frac{9 sin (\frac{π}{3})}{sin (\frac{π}{4})} = 12.02$ $c = (9 sin(pi/3)) / sin(pi/4) = 12.02$

Longest possible perimeter $P = 9 + 12.29 + 12.02 = 33.21$ $P = 9 + 12.29 + 12.02 = 33.21$

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of 9, what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Humanities

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Two corners of a triangle have angles of 5π12 (5 pi )/ 12 and π4 pi / 4 . If one side of the triangle has a length of 9, 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 $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of 9, what is the longest possible perimeter of the triangle?