Two corners of a triangle have angles of $\frac{7 π}{12}$ $(7 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . 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 $\frac{π}{4}$ $pi / 4$ . 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

1538 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-19T05:49:11

Longest possible perimeter of the triangle is

$P + a + b + c \approx 34.7685$ $color(blue)(P + a + b + c ~~ 34.7685$

Explanation:

enter image source here

$ˆ A = \frac{7 π}{12}, ˆ B = \frac{π}{4}, s i d e = 8$ $hatA = (7pi)/12, hatB = pi/4, side = 8$

To find the longest possible perimeter of the triangle.

Third angle $ˆ C = π - \frac{7 π}{12} - \frac{π}{4} = \frac{π}{6}$ $hatC = pi - (7pi)/12 - pi/4 = pi/6$

To get the longest perimeter, smallest angle $ˆ C = \frac{π}{6}$ $hatC = pi/6$ should correspond to side length 8#

Using sine law, $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b / sin B = c / sin C$

$a = \frac{c \cdot sin A}{sin C} = \frac{8 \cdot sin (\frac{7 π}{12})}{sin (\frac{π}{6})} = 15.4548$ $a = (c * sin A) / sin C = (8 * sin((7pi)/12)) / sin (pi/6) = 15.4548$

$b = \frac{c \cdot sin B}{sin C} = \frac{8 \cdot sin (\frac{π}{4})}{sin (\frac{π}{6})} = 11.3137$ $b = (c * sin B) / sin C = (8 * sin(pi/4) )/ sin (pi/6) = 11.3137$

Longest possible perimeter of the triangle is

$P + a + b + c = 15.4548 + 11.3137 + 8 = 34.7685$ $color(blue)(P + a + b + c = 15.4548 + 11.3137 + 8 = 34.7685$

Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of $\frac{7 π}{12}$ $(7 pi )/ 12$ and $\frac{π}{4}$ $pi / 4$ . 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 (7 pi )/ 12 7π12 (7 pi )/ 12 and pi / 4 π4 pi / 4 . If one side of the triangle has a length of 8 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 $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $8$ $8$ , what is the longest possible perimeter of the triangle?