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

Question

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

1 Answer

Impact of this question

1250 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-19T07:37:30

$Longest possible perimeter = 8 + 20.19 + 16.59 = 44.78$ $color(brown)("Longest possible perimeter " = 8 + 20.19 + 16.59 = 44.78$

Explanation:

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

To get the longest perimeter, side 8 should correspond to the least angle $\frac{π}{8}$ $pi/8$

Applying the Law of Sines,

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

$\frac{a}{sin (\frac{7 π}{12})} = \frac{8}{sin (\frac{π}{8})} = \frac{c}{sin (\frac{7 π}{24})}$ $a / sin ((7pi)/12) = 8 / sin (pi/8) = c / sin ((7pi) / 24)$

$a = \frac{8 \cdot sin (\frac{7 π}{12})}{sin (\frac{π}{8})} \approx 20.19$ $a = (8 * sin ((7pi)/12)) / sin (pi/8) ~~ 20.19$

$c = \frac{8 \cdot sin (\frac{7 π}{24})}{sin (\frac{π}{8})} \approx 16.59$ $c = (8 * sin ((7pi)/24)) / sin (pi/8) ~~ 16.59$

$Longest possible perimeter = 8 + 20.19 + 16.59 = 44.78$ $color(brown)("Longest possible perimeter " = 8 + 20.19 + 16.59 = 44.78$

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

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